Put the potatoes in a steamer basket in a large pot with enough water to just come through the bottom of the steamer basket. Bring the water to a boil and cook, partially covered, until the potatoes are tender but not soft, 20 to 30 minutes. (Alternatively, the potatoes can be baked in a preheated 400-degree oven until tender, about 40 minutes).
Remove the potatoes and let them stand just until cool enough to handle. (The hotter the potatoes are when they are peeled, and riced or milled, the lighter the gnocchi will be). Working quickly and protecting the hand that holds the potatoes with a folded kitchen towel or oven mitt, scrape the skin from the potato with a paring knife. Press the peeled potatoes through a potato ricer. Alternatively, the potatoes can be passed through a food mill fitted with the fine disc, but a ricer makes fluffier potatoes and therefore lighter gnocchi. Spread the rice potatoes into a thin, even layer on the work surface, without pressing them or compacting them. Let them cool completely.
In a small bowl, beat the egg, salt, pepper and nutmeg together. Gather the cold potatoes into a mound and form a well in the center. Pour the egg mixture into the well. Knead the potato and egg mixtures together with both hands gradually adding the grated cheese and enough of the flour, about one and one-half cups, to form a smooth but slightly sticky dough. It should take no longer than three minutes to work the flour into the potato mixture; remember, the longer the dough is kneaded, the more flour it will require and the heavier it will become. As you knead the dough, it will stick to your hands and to the work surface. Repeatedly rub this rough dough from your hands and scrape it with a knife or dough scraper from the work surface back into the dough as you knead.
Wash and dry your hands. Dust the dough, your hands, and the work surface lightly with some of the remaining flour. Cut the dough into six equal pieces and set off to one side of the work surface. Place one piece of dough in front of you and pat it into a rough oblong. Then roll the dough into a one-half-inch thick rope, lightly flouring the dough if necessary to keep it from sticking.
Slice the ropes into one-half-inch thick rounds. Sprinkle the rounds lightly with flour and roll each piece quickly between your palms into a rough ball, flouring the dough and your hands as needed to prevent sticking. Hold the tines of a fork at a 45-degree angle to the table with the concave part facing up. Dip the tip of your thumb in flour. Take one ball of dough and with the tip of your thumb, press the dough lightly against the tines of the fork as you roll it downward the tips of the tines. As the dough wraps around the tip of your thumb, it will form into a dumpling with a deep indentation on one side and a ridged surface on the other. Set on a baking sheet lined with a floured kitchen towel or parchment paper and continue forming gnocchi from the remaining dough balls. Repeat the whole process with the remaining pieces of dough. At this point the gnocchi must be cooked immediately or frozen.
Bring 6 quarts of salted water to a vigorous boil in a large pot over high heat. Drop about half the gnocchi into the boiling water a few at a time, stirring gently and continuously with a wooden spoon. Cook the gnocchi, stirring gently, until tender, about 1 minute after they rise to the surface. Remove with a slotted spoon and serve immediately.