The first time I went to Casa Montaña, two years ago, I was awed by the simple beauty of their preparation: the potatoes, fried to perfection, were crisp on the outside and creamy within. On my next visit, last fall, I asked the owner, Emiliano Garcia, for his recipe. One secret to his delicious version, he says, is that he cooks the spuds, which he's carved into six-sided nuggets, twice in olive oil—once to soften them and a second time to render them crunchy and golden. Then there's the sauce. Most places serve patatas bravas with only a chile-spiked tomato sauce called salsa brava (fierce sauce), the kind that made the dish famous in the 1950s when this tapa was invented at a Madrid restaurant called Vinicola Aurora. The dish soon caught on in other parts of the country; in the northeast, Catalan cooks added their allioli, or garlic-and-olive oil sauce, as a cooling counterpoint to the fiery salsa brava.