Heat the oil over a medium heat in a heavy casserole-type sauce pan. Add the onion and sauté, but do not brown, when the onions turn transparent add the beef and stir to sauté the meat with the onions, add the garlic and the caraway seeds
Remove the pan from the heat and add the paprika, stirring constantly to make sure it is absorbed well by the meat. The pan must be removed form the heat to add the paprika because paprika has a high sugar content, if added directly over heat it would burn and become bitter. Paprika is never added on direct heat.
Add the water and simmer gently for at least an hour. Check that the meat is cooked by testing a small piece. Add the tomatoes, pepper and potatoes. Season and simmer for 30 minutes.
For the Galuska:
Beat the eggs with 1 tsp salt and add the water. Add a little flour to make a smooth thick mixture then add the rest of the flour and beat with a wooden spoon until the dough is glossy and exceptionally smooth. Adjust with more flour is necessary, until the dough comes away from the sides of the bowl.
Place in a large grade grater on top of a large pan full of salted boiling water and force the dough through a grater directly into the water. Alternatively roll small dumplings of an even size using your fingers and drop them into the water. The galuska are done when they rise to the top of the water. Drain them in a colander and serve hot with some melted butter. Serve the goulash soup hot with the galuska.