Preheat the oven to 400°. Spread a 1-inch layer of salt in a small roasting pan. Prick the potatoes all over with a fork and arrange them on the salt in a single layer. Bake until fork-tender, about 11/2 hours. Remove them from the oven and slit them lengthwise to release their steam.

Line a large rimmed baking sheet with paper towels. As soon as the potatoes are cool enough to handle, scoop their flesh into a ricer or tamis and rice the potatoes onto the paper towels in a shallow layer. Let cool completely.

Working over a medium bowl, sift the all-purpose and cake flours with a large pinch of salt. Take 454 grams or 1 pound of the riced potatoes (don’t take all) and transfer the potatoes to a work surface. Sprinkle the sifted flour mixture over the potatoes and drizzle with the olive oil. Gently form the dough into a firm ball.

Test the gnocchi dough: Bring a small saucepan of salted water to a boil. Using your hands, form one 3/4-inch round (a single gnocco). Boil the gnocco until it floats to the surface, about 1 minute.

Using a slotted spoon, transfer the gnocco to a plate and let cool. It should be light and tender but still hold together. If the gnocco breaks apart in the boiling water, the dough has too little flour; add more. If the gnocco is tough and chewy, the dough has too much flour; cut in a little more of the reserved riced potatoes.

Line a baking sheet with paper towels. Divide the dough into quarters. Working with one piece at a time, gently roll the dough into a long rope about 1/2 inch wide. Using a sharp knife, cut the rope into 1/2-inch pieces. Roll each piece against the tines of a fork to make light ridges, if desired. Transfer the gnocchi to the baking sheet. Repeat with the remaining dough. Let the gnocchi stand at room temperature for 1 hour to dry.

Bring a large pot of salted water to a boil. Fill a large bowl with ice water. Add half of the gnocchi at a time and boil over high heat until they rise to the surface, then cook for 15 seconds longer. Using a wire skimmer remove from water and serve sautéed in butter or with your favorite sauce.

To refrigerate or freeze for later consumption, transfer the gnocchi to the bowl of ice water. Drain on paper towels and pat dry. Toss with oil and refrigerate for up to 3 hours or freeze the gnocchi on baking sheets in a single layer. Transfer them to an airtight container or resealable plastic bags and freeze for up to six weeks. To serve, sauté them in butter until heated through before proceeding.