"It's the difference between a Big Mac and a steak," says Alejandro Bulgheroni. I am at a wine tasting at the at the Bodega Garzon, a winery in the Maldonado Department of southeastern Uruguay. The oil and gas billionaire turned wine tycoon is explaining why he wants the vines on his vast estate to grow their roots deep into the soil.

The deeper you go, the richer the nutrients become compared to the blander top soil, he says. Here, the roots get into "the soul of the terroir" – ultimately producing a wine that is more fillet steak than McDonald's burger.

Everyone knows the Argentinians like their red wines beefy, after all, but Argentina's wealthiest man admits that, less than a decade ago, he knew nothing about winemaking. He didn't even drink it.

Since planting the first vines in 2007, Bulgheroni's 2,200 hectare "estancia" in the Tuscany-like hills of Garzón in south-east Uruguay has been transformed into a eulogy to wine. From growing the grapes to enjoying the end product, every aspect conforms to the overarching ethos of quality and sustainability.

Artificial herbicides and fertilisers have been shunned in favour of traditional, organic agricultural techniques.

It is the first winery in the world seeking LEED (Leadership in Energy and Environmental Design) certification for the entire facility, including its winemaking and hospitality, with nearly half the premises' energy requirement generated from wind and solar power.

Some 5,000 vines are crammed into every hectare for maximum yield, with only the best grapes entering the production line.

Instead of stainless steel, concrete tanks are used for fermentation because, Bulgheroni tells us, the rough walls “grab and preserve the microbiology of the grapes”, while concealing the heating pipes within the tanks' concrete walls "avoids shocking the yeast with extreme temperatures". The wine is then matured 15ft underground in untoasted French wood barrels.

These are people who take winemaking seriously.

And the results are pretty impressive, if the newest vintages unveiled at Bodega Garzón's grand opening in March are anything to go by.

Their latest red wine, a 2015 Tannat – Uruguay's national grape – is said to be an "exceptional vintage". It bursts with peppery black fruit flavours and toasted oak and vanilla undertones, while the 2016 Albariño – from the freshly harvested white grapes of the southern hemisphere – is almost impossibly fresh and zesty with a crisp, citrus tang.

Just don't expect to find any of it in your local supermarket. The aisles may be awash with bottles of Sauvignon Blanc from Chile and Malbec from Argentina, but Uruguayan wines are a rarity anywhere except among specialist wine retailers.

Although it is South America's fourth largest wine producer, only around three per cent of the country's wine is exported – and most of that goes to Brazil.

Bulgheroni is the first to grow grapes in Garzón and he has set his sights on a premium product to compete with the best of Uruguay's better-known neighbours. While he promises that it will eventually be exported in more significant quantities, for now there are only four stockists in Scotland: Exel Wines in Perth; Henderson Wines in Edinburgh; Top Cellar in Edinburgh; and Good Spirits Wine & Beer in Glasgow.

If you have deep (bottomless?) pockets, you can join Bodega Garzón's exclusive wine club for the princely entry fee of $180,000 (£127,000) and drink and dine in the winery's opulent lounges, private candlelit cellars or on the hilltop terraces with panoramic views over the vineyard. You can even create your own signature vintage.

For the non-millionaires, however, there are more realistic tourist options.

Besides the winery, which also houses an acclaimed restaurant, the Garzón empire includes Colinas de Garzónan, a boutique extra virgin olive oil production plant a few miles from the Atlantic coast. Here, visitors can enjoy the premium wines along with an authentic Uruguayan barbecue – or "asado" – cooked over an open wood fire on the banks of the Garzón Lagoon.

A trip to Colinas de Garzón is perhaps not for the squeamish – specifically those who would prefer not to see an entire animal carcass roasted over flames – but the setting itself is beautiful and the award-winning selection of olive oils, served with bread to dip, are mouthwatering.

The Garzón business actually started out in 1999 as an olive and almond farm, and also grows blueberries. At Colinas, you can tour the olive and almond groves, windmills and learn how olive oil is made.

Adventurous visitors can incorporate a hot-air balloon ride or a cycling tour, rounded off by a specialist tasting session of Garzón extra virgin olive oils and wines, accompanied by the house cheese selection and home-made bread.

No trip to the region is complete, however, without dinner at the fashionable El Garzón Restaurant, where one of South America's most famous chefs, Francis Mallman, has been cooking up a storm since the early noughties.

Situated quite literally in the middle of nowhere – or as Mallman describes it, "el Uruguay de adentro" ("authentic backcountry") – the cooking is bold and simple, using the traditional technique of cooking between two wood fires on iron griddles.

While the menu is dominated by meat – favourite dishes include salt-crusted chicken and lamb in a mustard and thyme crust – the chefs can turn round vegetarian options on request. Their char-roasted vegetables with fresh herbs and goat's cheese drizzled in olive oil dressings fresh from Colinas were delicious, and the Potatoes Anna – thinly sliced and doused in butter – are to die for.

If you have space after that, the supersized profiteroles – smothered in chocolate sauce and oozing mousse-like filling – are worth every bite.

And when it comes to where to stay, Uruguayans in the know will have only one answer: José Ignacio.

The chic fishing village has become one of South America's hippest spots, but remains blissfully underdeveloped compared to the skyscrapers crowding the ocean front in nearby Punta del Este.

In peak season, from November to February, it attracts celebrities, millionaire playboys and the well-heeled from across the continent. Singer Shakira is said to be a fan.

At Posado del Faro, the resort's bohemian boutique hotel overlooking the Atlantic, the staff bring you breakfasts of fresh fruit and bread on a tray to enjoy on your balcony. You can cool off in the swim-up bar and help yourself to drinks from the honesty bar in the lounge. The staff are attentive but unobtrusive, leaving guests to feel like they are relaxing in their own private villa.

A sign in the town cautions: "Aquí sólo corre el viento" ("Here, only the the wind runs"), in homage to the town's leisurely way of life. And with so much food and wine to be had, what else is there to do but relax?

Helen McArdle flew to Montevideo with British Airways and Iberia, from Glasgow. Flights start around £1048 return

She was a guest at at Posado del Faro in José Ignacio. Prices start at £1900 per person in low season (May-September), for seven nights based on two adults sharing a superior room