Prepare the dough according to the recipe and roll it out to the second-thinnest setting on a pasta-rolling machine. Cut it into 4 or 5 sheets of equal size, flour each sheet well, and cut them into 1-inch squares. Set aside on sheet trays lined with kitchen towels.
In the bowl of a food processor, pulse the spinach until finely chopped and add the ricotta, 1/4 cup of the grated cheese, and the nutmeg. Process until smooth, season with salt and pepper, and set aside in a warm place.
Bring 6 quarts of water to a boil and add 2 tablespoons salt. Cook the pasta squares in the boiling water and cook until tender yet al dente, about 3 minutes.
Drain the pasta and reserve 1 cup of cooking water. Add half of this water to the ricotta mixture, then add the pasta to the ricotta mixture, and mix well. Add more water if necessary to keep it from becoming too "tight", season with salt and pepper. Divide evenly among 4 pasta bowls and top with grated pecorino.
On a wooden board, place the flour in a mound. Form a well in the center and add the egg whites and salt. Add the water, a little at a time, while mixing in the flour and water with a fork. Using both hands, knead the dough into a ball, adding more flour as necessary, to obtain a smooth, pliable dough. Set the dough under an inverted bowl and let it rest 15 minutes.
Yield: 1 pound of noodles