Put the potatoes in a deep pot or saucepan in one layer. Cover with water at least 2 inches. Over medium-high heat, add 1 tablespoon salt and boil.
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Drain in a sink colander. Slice potatoes with a paring knife to release steam and moisture. Rest for 15 minutes until cool but not chilly.
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Sprinkle a little flour on a clean surface. Quarter the potatoes after peeling. Use a potato ricer on the floured surface. Make a well in the riced potato pile. Cool potatoes till warm.
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Sprinkle a scant cup of flour around the potatoes. Add salt to the well after sliding the egg yolk. Beat the egg with a fork and add the potatoes. Keep mixing lightly, adding flour around the edges.
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Softly press and pat the ingredients into a ball with your hands. It should be pliable, sticky, and “shaggy” rather than smooth. Add a tablespoon or two of flour to soft, sticky dough. Do not overwork or overflour the dough.
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Cover a rimmed baking sheet with a clean kitchen towel and semolina or all-purpose flour. Have a fork or gnocchi board ready. Sprinkle some flour on your work area and have a dish of flour handy.
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Roll the dough into a finger-thick rope using your hands. Make ropes from the remaining 3 dough pieces. Lightly dust ropes and cut into ¾-inch nuggets with a knife or dough scraper. Roll each nugget down the gnocchi board or fork tines.
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Air-dry the gnocchi for 30 minutes. While they rest, salt and boil a big kettle of water. Heat the sauce before cooking the gnocchi.
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Put a little sauce in your bowl. Drop gnocchi gently into boiling water. Cook in batches to minimize pot overload. After 30–45 seconds, the gnocchi will float. One should taste light and soft, cooked throughout, and without raw flour.
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Using tongs, put the gnocchi into six bowls to serve. Add more sauce on top, and if you want, add newly grated cheese to taste. Have fun!
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