Boil potatoes with all their skins in plenty of cold water for about 30–40 minutes. Drain them only when you can pierce them well with a fork. Drain potatoes, peel, and let cool. Mash the potatoes with a potato ricer.
If you used the right potatoes, the pulp will be dry. If a few drops of water come out when squeezing after you have mashed the potatoes, remove the water by pressing the potatoes with a clean cloth to dry them well. Let the mashed potatoes cool completely by placing them in a colander for at least 10 minutes. The colander will squeeze out the remaining droplets of water, and the cold puree will absorb less flour.
In a large bowl, add potatoes, salt, about 2 tablespoons of beaten egg, and flour. Knead very little and quickly, just enough time to get all the ingredients together (overwork makes the dough sticky!). Shape the dough into a ball and place it on a floured work surface.
Cut the dough into 7-8 parts and form cylinders 2-3 centimeters thick. If the cylinders stick to your hands, lightly flour your hands. Cut each cylinder into 2 cm pieces to make smaller cylinders.
These can be ready-made gnocchi, but if you prefer classic striped gnocchi, proceed as follows. Take a lightly floured fork, slide the gnocchi along the inside, pressing lightly with your index finger. Arrange them on a tray covered with a clean cloth and let the gnocchi rest in the air for about 30 minutes, so they will dry out further. Meanwhile, prepare the tomato sauce.