Boil the potatoes in their jackets, drain, peel and put through a ricer or food mill. While the potatoes are still warm, blend in the flour, add the egg, egg yolk, butter and salt.
Place the potato mixture on a floured board and knead lightly; the dough will be soft. Roll the dough in 1″ thick sticks about 10″ long. Cut each roll into 3/4″ pieces.
Rub each pieces of dough lightly over the coarse side of a cheese grater. In a large pot of boiling salted water, cook the gnocchi until they rise to the top of the water. Using a slotted spoon, remove the gnocchi to a warm bowl. Sprinkle with Parmesan cheese, top with tomato sauce and serve at=