Sauté onions in butter over high heat until brown, constantly stirring. Add cubed meat, paprika, 1 tsp. salt, and pepper. Continue stirring until meat is browned. Cover pan tightly, reduce heat and simmer 1 1/2 hours. Sprinkle flour over meat mixture; stir in well. Add 3/4 cup water and continue simmering for an additional 15 minutes. Seasoning or more water may be adjusted at this time if necessary.
For dumplings: combine 2 cups flour, eggs, 1/2 tsp. salt, oil and warm water; beat until mixture is smooth and blistery. Cover and set aside for 15 minutes. Drop spoonfuls of batter into a pot of boiling, salted water and cook about 10 minutes; drain, blanch under running water and drain again. Serve goulash over dumplings.
