Step 1

In a large pot, combine the potatoes and 4 quarts water. Bring to a boil over high, then stir in 1 tablespoons salt. Reduce to medium-high and cook, stirring occasionally, until the potatoes break apart when pierced with a knife, 15 to 20 minutes. Meanwhile, set a cooling rack in a rimmed baking sheet and line the rack with kitchen parchment.

Step 2

Drain the potatoes in a colander, shaking the colander to remove excess water. Return the potatoes to the pot and cook over low, gently folding with a silicone spatula, until the potatoes look dry and slightly powdery and the bottom of the pot is coated with a thin film of potato starch, 3 to 4 minutes. Transfer the potatoes to the prepared cooling rack in an even layer. Cool to room temperature. Meanwhile, in a small bowl, whisk together the flour, baking powder and 1/2 teaspoon salt.

Step 3

Weigh out 1¼ pounds (about 4 cups) of the cooked potatoes into a large bowl; save the remainder for another use. Discard the parchment from the baking sheet, then line with fresh parchment and coat with 1 tablespoon of oil; set aside. Add 1/2 teaspoon salt to the potatoes and pass the potatoes through a ricer or a food mill fitted with the fine disk back into the bowl, or mash them with a potato masher until as smooth as possible.

Step 4

Sprinkle the flour mixture evenly over the mashed potatoes. Using your hands, lightly toss the potatoes to evenly distribute the flour mixture. Add the egg and gently mix with your hands until the egg and flour mixture are incorporated. Turn the dough out onto a lightly floured counter and gently knead just until smooth; do not overknead. Using a bench scraper or knife, divide the dough into 4 pieces.

Step 5

Roll 1 piece of dough into a rope about 16 inches long, then use the dough scraper to cut it into 16 pieces. Place the pieces in a single layer on the prepared baking sheet. Dip the back of the tines of a fork into flour, then gently press into each piece to create a ridged surface. Repeat with the remaining pieces of dough.

Step 6

Set a wire rack in another rimmed baking sheet and line the rack with kitchen parchment. Coat the parchment evenly with the remaining 2 tablespoons oil. In a large pot, bring 4 quarts water to a boil and stir in 3 tablespoons salt. Add half of the gnocchi, return to a boil and cook, stirring gently and occasionally, until the gnocchi float to the surface. Cook for 1 minute, then use a slotted spoon to transfer the gnocchi, letting excess water drain, to the prepared rack. Return the water to a boil and repeat with the remaining gnocchi. Let the gnocchi cool for at least 15 minutes before using.