The truth is, anyone coming to a place this beautiful to ski should happily eat a spag bol and thank their lucky stars. Yet Alta Badia, in the heart of the Dolomites, attracts the kind of clientele that likes its lilies gilded. This is one of the ritziest Italian winter resorts, so while it has some of the most expansive ski areas in the world, in the middle of a Unesco natural world heritage site, the locals are eager for visitors to know they do pretty good food, too.

Arriving here via the flight to Verona is a red herring. After an hour at continental speeds on the autostrada towards the northernmost province of South Tyrol, Roman amphitheatres and Capulet balconies feel impossibly distant from the apple orchards that pave the way to the Alpine slopes. Another hour or so later and you are in Alta Badia, as Italian as sauerkraut and strudel. The legacy of the collapse of the Austro-Hungarian empire and the troubled decades that followed is a region that still feels more Germanic than part of the Italian state, with a wealth to match that might explain the preponderance of Michelin-starred chefs, three even in the Alta Badia ski resort: a trio billed as the Dolomitici – or Dolomighty ones.

The German spoken officially with Italian throughout the province gives way in the Alta Badia ski region to Ladin, an ancient Romance language preserved and spoken by a majority in the valleys around Corvara. Food here reflects the memory of a more difficult mountain existence as well as its prosperity today: the two menus it promotes for skiers are, first, the more delicate, nuanced dishes invented by its guest chefs; second, the local, traditional food best appreciated for surviving hiking up a snowy mountain.

For the latter, the best-known Ladin restaurant is Maso Runch-Hof. Runch (pronounced to rhyme with bunk, rather than massive lunch) is the home and institution of one family. Frau Nagler and sons cook while Herr Nagler is front of house, with the face of a benevolent Sid James and an alarmingly large bottle of home-made schnapps, brought to help digest the seven courses on the fixed menu.

My fellow diner – a local, Ladin connoisseur – testifies to the quality of Runch's specialities of tutres and canci. These are varying shapes and sizes of doughnut- and pancake-like concoctions as well as ravioli: spinach, cheese or sweet poppy-seed fillings wrapped in various types of batter, coming plate after plate. Runch could give Aviemore hoteliers hope for a tasting menu built around the deep-fried Mars bar. The host and waitresses look bemused as we decline extra helpings, but the volume of the average human stomach could surely manage little more than the excellent, hearty panicia barley soup and pücia crispbreads and a nibble at the main course, a ham hock that would keep an entire von Trapp family busy.

It feels slightly surreal, even before a middle-aged man in shorts and a green-feathered cap comes in with his accordion to sing. But the high camp of the Alps is not restricted to Ladin agriturismo: the hotel La Perla, located metres from the Cap Alt cable car, puts on a bizarrely enjoyable show for its guests. Not in its L'Murin barn-turned-club complete with go-go dancers; nor even in its underground spa, where ageing, naked Germans wade solemnly anticlockwise between icy and warm paddling pools to boost their circulation. La Perla's real coup de theatre is its wine cellars: and while there are some proud collections in its 30,000 bottles, what truly astonishes is the effort and imagination that has gone into creating something entirely unexpected.

Without overly spoiling the surprise for future guests, it's as if the hotel had Adam Curtis and Willy Wonka on stage design. Calling it the Mahatma cellar may be something of a dubious tribute to the ascetic Gandhi, but this is a tour to delight non-drinkers as much as wine gluggers, from the moment the sommelier starts dancing in the first vault.

Up the cellar's fireman's pole is the Stüa de Michil – La Perla's own Michelin-starred restaurant, where concoctions such as veal tongue and octopus are served up for the gourmand (with one refined main dish costing more than a night at the Runch). This room is one of numerous stubes, or traditional parlour rooms, where guests can dine: each is different, but with the essential decor of wooden panels on floor, wall and ceiling, a throwback to the past when only one warm room in the house would serve, thus insulated, as a place for the family to congregate, cook, eat and sleep – on top of the oven.

As if to lure the holidaying gastronome out of the resort and on to the ski slope, Alta Badia's plusher mountain huts have also launched skiing taste trails – one traditionally Ladin, one the creation of a consortium of South Tyrol's Michelin-starred sons. The Ladin menus can be found in the slopes leading up to the magnificent peak of Santa Croce: close up, the Dolomite rock is a more colourful, coffee stone than the sombre grey it appears when viewed across the Alps. In this former place of pilgrimage, where a simple Catholic chapel still stands, skiers can now walk up the last stretch from the highest lift to try Ladin delicacies at the Crusc hut – although the pössl I tried would be recognised through the Alps as what Austrians call Kaiserschmarrn, a thick mishmash of shredded pancakes and red-fruit compote. Elsewhere, for the chef chasers, are 11 huts in each of which one dish has been specially created by a Michelin-starred son of Tyrol. At the Pralongia, for example, there is pork belly with Indian spices on kraut with a grappa-soaked plum sauce – and, given ski-slope mark-ups, they are not unreasonably priced at €12-25.

Then you've just got to ski back down. The slopes here aren't as vertiginous as some. There are some great long red runs, including the majority of the 26km Sella Ronda circuit that can be skied in one energetic day. A combined Dolomiti Superski pass links 1,200km of pistes in a dozen resorts around Alta Badia, joined by long stretches of almost horizontal lifts. That means many chair lifts give the disconcerting sight of rows of skiers heading towards each other rather than all going up a mountain – grateful, perhaps, for a chance to digest all that rich food.

Essentials

British Airways (ba.com) flies daily from Gatwick to Verona, with fares from £80.60. Hotel La Perla (hotel-laperla.it) has rooms from ¤320 per night, including breakfast. For more information on South Tyrol, go to suedtirol.info