Some popular Slovak recipes are bryndzové halušky, the Slovakian national dish, and kapustnica, a traditional sauerkraut soup served on Christmas. Slovak-Republic.org publishes simple recipes for both bryndzové halušky and kapustnica.
Bryndzové halušky is similar to gnocchi and is made with sheep cheese. To make bryndzové halušky, peel and shred three potatoes and stir into a dough with 5 tablespoons of flour, one egg, 1 tablespoon of salt and some water. Drop 2 1/2-centimeter pieces of the dough into salted boiling water and cook for a few minutes until they float to the top. Remove the boiled halušky with a strainer and serve topped with melted bryndzové cheese and fried bacon with some of the bacon grease.
To make kapustnica, put 1/2 kilogram of sauerkraut into a large pot with a liter of water. Mash two cloves of garlic into a paste and add to the pot along with two small pieces of onion. Add black pepper, caraway seeds, cloves and nutmeg to taste along with two bay leaves and some dried mushrooms. Add 1/2 kilogram of pork, cook for about 20 minutes and then add a chopped sausage to the pot. Add red pepper and paprika to taste, then cover the pot and simmer for about 30 minutes. Season to taste with salt and serve with sour cream.