A family-run inn that began as a miners' tavern in 1567 has become one of Austria's most remarkable alpine escapes.

Halfway up the majestic Wilder Kaiser mountain range, my guide Lois Manzl – who was born and bred right here in Tyrol – decided he wanted to play his trumpet for a while. Dressed in lederhosen he belted out a traditional alpine song as I caught my breath and felt sweat trickle down my body. I thought about the reward Manzl had promised me at the end of the climb: a 300-year-old hut sitting just at about 5,000ft (1,524m) above sea level, below the enormous petrous cliffs of the mountain. "You're going to like it," he said between bursts of notes, as I traipsed behind him.

He stopped playing and looked at me. "Kids absolutely hate hiking," he told me. "When I have kids on one of these hikes, they almost always ask me why I chose to be a mountain guide for a living. And so I tell them: I was very bad in school and was condemned to do this for a living." And then he burst out laughing.

The closest you might come to a real-life version of The Sound of Music or Heidi would be a few days at Stanglwirt, a one-of-a kind resort in Austria's Tyrolean Alps, where this guided hike with Manzl is just one of many diversions on offer. As a travel writer, I tend to use hotels for what they were originally intended: a place to sleep while I explore a destination. But the longer I spent at Stanglwirt, the more I felt like staying put. In fact, with the exception of the hike, I didn't leave the property during my four-day visit.

Founded in 1567 as a tavern for miners, Stanglwirt became a fully-fledged inn around 1720. Two years later, it was taken over by the Hauser family, who have been running it ever since. But to call the 170-room Stanglwirt simply a "hotel" would be a misnomer. When I encountered Balthasar Hauser, the 80-year-old owner and patriarch in a hallway one day, he told me, "Stanglwirt is not a hotel with an organic farm," he said, wagging his finger at me. "It's an organic farm that happens to have a hotel."

He had a point. Set on 132 hectares of arable land and pastures, Stanglwirt produces its own cheese, milk, yoghurt and beef. "The creamier the cheese, the shorter the life span," said Anna Aichinger, the on-site cheesemaker, during a tour of the cheese cave. "But because I'm only producing cheese for the hotel, it gets eaten very quickly." She handed me a thick slice of Bergkäse, a semi-soft mountain cheese made with raw cow's milk and speckled with herbs. It was the creamiest cheese I'd ever tasted.

Eco-friendly Stanglwirst has been sustainable since long before it became a buzzword in the travel industry. But its dedication to sustainability goes beyond its methods of food........

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