Bring a large pot of salted water to a boil. Drop in potatoes and cook until tender but still firm, about 15 minutes. Drain, cool slightly, and peel. Mash potatoes with fork, masher or in ricer. Place in large bowl and make a well in the center. Put butter in well and allow to melt. When mashed potatoes have cooled, knead in enough of the flour to make a soft dough.
Divide dough into fist-sized portions. On a floured surface, roll each portion into a long rope. Cut the ropes into one-inch pieces. Roll each piece with a fork for a distinctive texture.
Bring a large pot of lightly salted water to a boil. Drop in gnocchi and cook for 3 to 5 minutes or until they float to the top; drain and serve with tomato sauce.