Ages ago, I studied in Madrid. Our house mom was not a good cook, but she did introduce me to two classic dishes: fabada asturiana and tortilla española, a rib-sticking mixture of eggs, onion, and yellow potatoes. Smitten Kitchen posted a great version of it here; it’s easy, cheap, and satisfying (and keeps well in the fridge).
The second must-try is leek potato soup (below). I used this Emeril Lagasse recipe, but omitted the creme fraiche, added 2 more strips of bacon, used black pepper instead of white, and olive oil instead of butter. It doesn’t look that appetizing (“try the grey stuff, it’s delicious!“), but the soup’s flavor is as complex & savory as its exterior is drab.