Outside of the Slobodné Vinárstvo winery in Hlohovec, western Slovakia, an affectionate German Shepherd named Luna insinuates herself in and out of our legs. The winery's co-owner Agnes Lovecka and I sip strong black coffee at a table freighted with sweet cheese and vanilla cakes, korbácik (an exceptionally stringy cheese), parenica (rolls of smoked cheese), charcuterie from a nearby farm and treska , a cod salad – which I'm fittingly informed is instrumental in soaking up hangovers.

"Breakfast wine!" Mišo Kuropka bellows. Agnes' brother-in-law and business partner arrives at the table barefoot in a striped Breton shirt and wraparound cycling glasses, brandishing three bottles of off-market pinot gris pét-nat.

The wine is a straight razor cut of freshness, its skin-contact acidity and effervescence bringing to mind another breakfast drink: mimosas. Over in the distance, chef Santiago Lastra and his brother Eduardo wheel wagons around the back of an outbuilding to the whine and chatter of power tools.

The wine is a straight razor cut of freshness, with skin-contact acidity and effervescence

Santiago, a chef and restaurateur who recently launched his long-awaited first permanent restaurant KOL in Marylebone, has brought me here to taste his house wines, which are being made for him by the team at Slobodné.

The chef famously cut his teeth working with René Redzepi as project manager of Noma Mexico in Tulum, and now, aged 30, his skills have taken him around the world, with the past two years seeing him cooking in 27 different countries.

His vigorous interest in the produce, the history and the people of the countries he visits has led him to foster deep and impactful relationships across the globe, and it's this – along with a close friendship with the sisters Agnes and Katka and their partners Mišo and Andrea at this Slovakian winery – that has borne fruit in the shape of four exclusive bottlings for KOL: white, orange, rosé and red.

As the food is cleared away, weathered brown deeds and ancient maps are laid out across the table, detailing the land as it was when originally purchased in 1912. The Lovecka family's history – and, more broadly, the history of Slovakia – is one of fracture and disruption.

While nursing flutes of pét-nat, Agnes, her sister Katarina Kuropkova and Mišo bring me up to speed. The saga of the Lovecka's family farm begins in 1912, when it was originally purchased by their great uncle Peter Herzog, a man committed to agriculture and the land.

Their grandfather Eduard departed for Prague to study intervals in classical music, they tell me, and when the Nazis invaded Slovakia and Peter, a partisan, died in an uprising fighting a puppet government run by controversial head of state Jozef Tiso, Eduard inherited the deeds, which he turned over to his daughter.

From the time when communism swept through Czechoslovakia in 1948 until the peaceful Velvet Revolution brought it to an end 40 years later, to belong to a landowning family was viewed as a stigma – a cross to bear best hidden from prying eyes. The certificates of ownership were secreted away in a cubby space behind a partition and mostly forgotten.

Then, in 1989 when communist rule came to an end, the family scrambled to find the deeds in order to receive restitution of the property. A wall beneath the stairs was knocked down and the box was recovered.

Initially the family was accustomed to living in cities and had little interest in the 300-hectare farm, which had been left in a terrible state. But over the years, disenchantment with urban living began to encroach. Lovecka took courses in winemaking and Slobodné Vinárstvo (which translates as 'Freedom Winery') created its first wine (a blaufrankish or 'frankovka') in 2010.

In 2012, 100 years after Peter Herzog originally bought the land, they released Interval 100 – a 100% riesling bottling that Mišo touts as one of his favourites. The wine is a bracing blend of nuttiness on the palate with a bright, green-apple finish.

I ask Mišo whether the wine's name has anything to do with Eduard. He tells us the name 'Interval' was a tribute to Agnes and Katarina's grandfather, for his musical studies; for the interval of history between when the land was purchased; and for the interval between the methods employed then in winemaking and Slobodné's current low-intervention approach. The Partisan Cru – a cuvée of Lemberger, C/S and Alibernet – is similarly in tribute to Peter.

KOL restaurant: Slobodné's Miso Kuropka
KOL restaurant: Slovakian winery Slobodné Vinárstvo

But there are two other siblings on the farm, too. In the distance, Santiago and Eduardo are wearing matching umber-coloured T-shirts. Eduardo, a former engineering student, has built a frame on which to suspend an entire butterflied lamb over an open flame.

While preparing dinner, Santiago has also made us a lunch of grilled sourdough tortas with suckling pig carnitas, lightly fermented cabbage spiked with gossamer-thin habanero chillies alongside wild purslane and fat hen (a herb otherwise known as white goosefoot) foraged from the farm.

Cooking has played an integral part in Santiago's life since his father passed away during his teenage years, when he attempted to cheer up Eduardo and his mother by preparing pimped-up recipes gleaned from the back of a Ritz crackers box.

Obviously, his technique has come on leaps and bounds since then, but the same generosity of spirit and DIY adventurousness prevails in everything he does. Eat one of his freshly pressed tortillas and it's hard not to feel the love.

That love applies to the winemakers he works with. At KOL, he's playing a bit of the enfant terrible ; peddling a subversively specific wine list, comprised almost entirely (champagnes aside) of Central and Eastern European wines, and arranged according to the varying degrees of colour. It's perhaps a window into his outlook that selections from Spain and France fall into the 'rest of the world' category.

The Magula vineyard has a similar history to that of Slobodné. Later, we drive through Trnava, a city of contrasts where borough walls and Gothic spires vie with faded smokestacks and newly minted shopping malls, on our way there.

Driving along country lanes circumscribed by Lawson cypress through golden fields of wheat and corn, we approach a thin band of mountains, the Small Carpathians, where viticulture has been established since Roman times. As we wind our way through black pine and boxwood, blue spruce and European yew, a nuclear power plant hoves into view, grossly juxtaposed with the bucolic Rose and Wolf Valleys.

Lastra started out cooking pimped-up recipes gleaned from the back of a Ritz crackers box

Magula is also very much a family affair. Vladimir Magula Sr snips around the yard inspecting plants while Vladimir Magula Jr walks us through two vineyards named after his sons Hugo and Maxim. We retire from the 35-degree heat into the cellar and taste our way through an array of low-intervention wines, nibbling on local sourdough and excellent bryndza, a soft sheep's milk cheese. None of wines are filtered, with zero or very few sulphites added.

Their grüner veltliner is not retiring. Aged in stainless steel and then amphora – a clay pot buried in the ground, most commonly found in Georgia – it is unabashedly full-on. Oranžový Vlk (Orange Wolf) is an orange wine made from grüner veltliner, welschriesling and the local variety, devín, that's similarly snappy.

Magula Jr is very excited about the blauer portugieser varietal, as it features heavily in one of his favourite books, Red Wine by Frantisek Hecko, a classical communist family saga set in one of the nearby valleys. Magulo Jr uses carbonic maceration to tease out a juicy flavour from the grape, with notes of strawberries and red fruits.

Magula's history is similarly rich, and sheds further light on the complex history of winemaking in this part of the world. His grandfather Joseph Husar had bought the property in 1931 and adopted trailblazing processes to grow wines in the region, before losing it in 1948.

When asked if he thinks the interlude of communism on his family's winemaking had led to them adopting the less classical techniques used in Slovakia in favour of innovative low-intervention techniques such as amphora, he replies, "Winemaking is one of the industries most formed by myth and prejudice. The disruption of history separated us from this. When I review my oenological notes I realise that most of it was nonsense."

KOL restaurant: the Lovecka family

Meanwhile, back at Slobodné Vinárstvo, Agnes Lovecka says very much the same thing. Their self-taught wine education has led them "to break with local winemaking dogma." Instead, they puzzled out what was going on in the wider world through reading books and magazines in English, becoming low-intervention autodidacts in the process.

That evening, as the sun is setting over the cornfields, a candlelit table has been transformed into a veritable horn of plenty, heavily laden with bulbs of garlic, ears of corn, cabbage, pumpkins, tomatoes, purple and white carrots along with dangerously hot cerise-coloured habanero chilli.

Santiago, with his wolfish grin and a shock of black hair, apologises for his bad penmanship as he draws our attention to the menu for the evening, which has been scribbled onto a chalkboard.

A few others have joined, such as Modal Wines distributor Nic Rizzi and Anglothai chef John Chantarasak, and the prevailing vibe is Dionysian.

Large-format bottles of the Interval Rieslings and Alternativa Frankovkas are circulating rapidly as the first plates of the Lastras' food arrive on the table: an invigorating gazpacho of tomato and apricot cut with a pinot gris vinegar made on the farm; a ceviche of local celeriac, courgette and pumpkin seeds with a fermented ramson juice; and thick-cut tomatoes and wild cherries dressed with kombucha, wild garlic and lamb fat that positively detonates with umami.

But the main event is indubitably the tacos . Blue corn tortillas and steamed cabbage (which translates as 'kol' in Spanish, hence the restaurant's name) are wheeled out to the table to swaddle the lamb asador.

Coal-roast tomatoes and habanero sauerkraut are provided to prop it up, as well as chorizo and Slovak cheese. We douse the whole situation in an excellent array of sauces, including a 'seaweed macha' made with rattlesnake chilli, oil, peanut, dulse seaweed and Kentish honey and a borracha sauce made with whisky, ancho, adobo, chipotle and Granny Smith apple.

The sun has touched down behind the horizon and there's something feral about the way we stalk around the lamb carcass, pilfering morsels, paws moistened by wine and meat. Agnes begins to resemble a World War Two medic: any time my glass begins to run dry she swiftly jogs over with a magnum to patch me up.

At the end of the evening, she delivers one last speech. "This was all made possible when a few years ago we met Santiago Lastra and became family," she says. "Thank you deeply for coming and for sharing this magical night celebrating friendship, family and freedom."

Spending time with Lastra in a place like this, it becomes clear what his aims are: to showcase producers like Slobodné that share his locavore ethos; to combine a sense of Mexican bonhomie with an appreciation of contemporary London restaurant culture; and, more than that, to create a family that transcends borders, cuisines and dogma. To anyone who has eaten at KOL since it finally opened, or plans to in the coming months, you'll surely agree he's done just that.