(See also: Tomato-Porcini Sauce.)
Bake potatoes until tender. While hot, cut in half and scoop out pulp. Work pulp through ricer into large bowl (or mash using up-and-down motion only). Using fork, stir in eggs. Blend in 1/2 cup flour. Turn dough out onto work surface. Gradually knead in 2 cups flour. Continue kneading until smooth and elastic, about 10 minutes. Shape dough into 6x4-inch loaf. Cut loaf into 1-inch strips. Roll strips into cylinders 1/2 inch in diameter. Cut cylinders into 1 1/4-inch pieces. Boil 1 piece 2 to 3 minutes. If piece falls apart, add more flour to dough 1/4 cup at a time until pieces hold together when boiled. Using floured fork, press tines downward into each piece so it curls around fork. Arrange in single layer without touching on generously floured towel. Let gnocchi stand 3 to 4 hours at room temperature to dry.
Bring water and salt to boil. Add gnocchi. Stir gently with wooden spoon. When gnocchi come to surface let cook 2 minutes. Drain well. Place on platter. Spoon Tomato-Porcini Sauce over. Dot with butter. Sprinkle with Parmesan.