Boil the potatoes in their skins until soft, peel them while they are still warm and pass them through a sieve. Let them cool a little, mix them with the beaten eggs, flour and a little salt and knead the dough until it no longer sticks to your hands.
Now, with floured hands, roll finger-thick rolls and cut them into pieces two centimeters long. Place these pieces of dough one by one on a fork held in the left hand. With the thumb of the right hand, press the piece of dough so that it curls up a bit, creating the typical shell-shaped gnocchi with the pattern of fork tines.
Boil them in enough salted water for a few minutes until soft, then lift them out with a slotted spoon as soon as they rise to the surface. Let them drain well and put them in a preheated baking dish.
These gnocchi taste best when covered with melted butter, in which a sage leaf can be steamed, and sprinkled with a generous amount of grated Parmesan cheese. They can also be served with tomato or minced meat sauce.