Tulipan is definitely the best Korean restaurant in Madrid and by far the best I've ever eaten at anywhere.
They only have a fixed menu (18 euros/person more or less) that features fresh, seasonal plates with many of the veggie dishes coming straight from the restaurants gardens.
You always start with a large spread of small, cold appetizers; things like kimchi, seaweeds, spinach, chili peppers, sprouts, and various vegetables in chili sauce.
Then they bring out three main plates. During my visit (remember, the menu is always changing) we had pork and spinach dumplings (delicious!), an addictively-good spring onion omelette, and sweet potato noodles with meat and vegetables.
To finish, you always get a sizzling tray of meat, noodles, rice, and vegetables, all served in a sweet and spicy broth and put to boil right at the table. You'll leave filled to the gills with food but you never feel heavy or sleepy.
This is one place I'd recommend 100% to anyone in Madrid who loves authentic Asian food!