Preparation

Cook the potatoes:

• Fill a pot with lightly salted cold water, add the potatoes, and simmer them until very tender, about 35 minutes. Drain them in a colander set into the sink and let them rest in their own steam until they’re cool enough to handle. Peel them.
• Pass the potatoes through a ricer or the medium plate of a food mill (or through a basket sieve, pressing with a rubber spatula). Add the egg, cream, salt, and nutmeg to the potatoes, mixing well to combine.

Mix the dough

• Pour the flour onto a work surface and make a well in the center. Add the potato mixture to the well
  

• With a pastry scraper, cut the flour into the potatoes. Work the dough by cutting, pressing, and turning it over on itself with the pastry scraper.
  

• Keep working until the dough comes together and is soft, supple, and slightly elastic.
  

• Roll the mass into a large log and cut the log into four equal parts. Let the dough rest for 10 minutes.
  

Shape the dough into dumplings

• Roll the logs into ropes about 3/4 inch in diameter, cutting them in half if they’re too long to work with.
  

• Cut the ropes into nuggets that are a generous 1/2 inch long. If some of the ropes swell as you cut others, roll them back down to the original diameter.
• Dredge a dinner fork in flour and tap off the excess. Hold a dough nugget between your thumb and forefinger, grasping at opposite corners. Position it so a corner points toward you, diamond-like. Starting where the fork tines begin, and keeping your thumb perpendicular to the tines, roll the dough over the inside tines of the fork, changing from pinching with your thumb and forefinger to pushing gently with your thumb; you’re trying to create an ovoid shape.
  

• Let the dumpling fall off the fork, flicking it off gently with your thumb if needed. Your thumb will have shaped a dimple, and the tines will have scored ridges. Flour the fork again (or each dough nugget).
  

• Transfer the shaped gnocchi to a well-floured sheet pan and then cook them, freezing what you won’t use immediately. Gnocchi will hold in the refrigerator for up to 12 hours. If wrapped well, they’ll keep in the freezer up to 2 days.  (You needn’t thaw frozen gnocchi before boiling, but do boil them in batches.)
  

Cook and sauce the gnocchi

• You’ll have about 200 gnocchi, but you may want to cook smaller batches so your pot isn’t too crowded. Bring a large pot of lightly salted water to a boil and add the gnocchi. Let them simmer for about five minutes, or until they all float.
• Meanwhile, warm a large skillet over high heat and put in the butter. If you’re making the entire recipe, work in batches or in two skillets. Raise the heat and add the sage leaves, swirling them in the butter.
• Brown the butter (without burning it) to a deep amber, crisping the sage leaves during this process. You’ll see darker flecks of butter solids; this is fine. Add a squeeze of lemon and take the pan off the heat.
  

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• Drain the gnocchi thoroughly and toss them into the pan. Season with a little salt.
• Gently toss the gnocchi in the browned sage butter, stirring occasionally to make sure none is sticking to the bottom. Divide among eight warmed plates, drizzling any remaining brown butter over the pasta. Grate the Parmigiano over each portion and serve at once.