Boil potatoes in jackets. Peel when cool and grate or rice them. Add eggs, salt & flour. Beat the batter with a fork until fluffy. Chill. Roll lightly into balls 1" in diameter and drop gently into gently boiling salted water for 10 minutes. Drain well.
When you are rolling them dampen your hands with warm water and then they won't be sticky.
NOTE 1: My grandmother used to put croutons in the center of each dumpling and form the dumpling around it. My family prefers them just this way. To make it easy, I drizzle a little melted butter over large store-bought croutons and just use those. Any flavor you like.
NOTE 2: Leftover dumplings are even better the next day sliced and fried in butter on each side. Serve with leftover sauerbraten and gravy!