Place potatoes in a large pot. Add water to cover and bring to a boil over medium heat. Reduce heat and simmer until potatoes are easily pierced with a fork. Drain and let cool to room temperature. Then place in a self-sealing plastic bag and refrigerate overnight.
The next day, using a paring knife, scrape off and discard skins and any eyes or blemishes. Put potatoes through ricer. Measure out 12 ounces (375 g), or 2 slightly rounded cups (510 mL).
Using stand mixer fitted with beaters or the paddle attachment, place potatoes in mixer bowl. Mix on slowest speed for 1 minute, to a relatively smooth consistency. Gradually add flour, egg, Parmigiano-Reggiano and salt and pepper. Remove beaters or paddle and attach dough hook. On speed 2, knead, scraping sides of bowl as necessary, until dough is firm and pliable, about 3 minutes.
Divide dough into 4 equal pieces. Dust a clean work surface lightly with flour. With lightly floured hands, shape each piece of dough by rolling into a long rope the thickness of an index finger. Using a sharp knife or bench scraper, cut dough into pieces about 1/2 inch (1 cm) long. Dust lightly with flour or roll them lightly in flour on your work surface.
If you prefer indentations in your gnocchi, which help the sauce to cling, place a fork, tines pointing down, on work surface and press each gnocchi against the tines. You can also press them against the smallest holes of a cheese grater. Transfer to a plate dusted with flour. The pasta is now ready for use in your favorite recipe.
Like their pasta relatives, gnocchi should be cooked in a large pot (at least 8 quarts/8 L) in about 6 quarts (6 L) of well salted (about 1 tbsp/15 mL) rapidly boiling water. Use a flat bench scraper to scoop up gnocchi and drop into the boiling water.
Gnocchi are cooked to the al dente stage (about 6 minutes) and drained. Because they are tender, drain with care. Lift from water with a spider or large, shallow perforated scoop and transfer to a colander. If pouring directly into a colander, pour slowly and gently. Reserving some of the cooking water allows you to adjust sauces to the proper consistency, very much as you would use reserved pasta cooking water.
After the gnocchi are cooked you can serve them immediately with your choice of sauce.
If you prefer to use them later, place on a lightly greased baking sheet and let cool to room temperature. Once they are cooled, cover with plastic wrap and refrigerate for several hours or overnight. When you’re ready to serve them, add cooked gnocchi to warm sauce and, using a nonstick spatula, toss gently to coat evenly.
If you prefer, you can place the pans of pasta in the freezer. Once frozen, transfer it all to a resealable plastic bag lightly sprayed with vegetable oil on the inside. Gnocchi will keep, frozen, for up to 1 month. Before using, defrost in the refrigerator overnight or at room temperature.