Boil the potatoes in salted water, then mash them thoroughly with a fork while still hot. Let them cool and work to a stiff paste on a board with the flour, the egg and the grated Parmesan. Roll in the shape of a long sausage, the thickness of a thumb. Cut this into 1 inch lengths and let them stand for about 1 hour or more to dry. Boil in salted water or stock for about 10 minutes until they have all risen to the surface. Drain, and sauté or fry lightly in butter, sprinkling them with breadcrumbs and Parmesan cheese. A tomato sauce is often served with this.