Preparation

Make the dough

• Cover the potato with about 1 inch of water in a saucepan. Bring to a rolling boil over medium-high heat, reduce to a gentle boil, and cook until easily pierced with a skewer, 35 to 40 minutes. Drain and let cool briefly. Peel the potato as soon as you can handle it. Pass the potato through a ricer into a large bowl, spreading it out to help any steam escape.
• Sift the flours into a large bowl, and whisk in 1-1/2 tsp. salt. add the still-warm potato and egg, and mix to combine; the dough will be crumbly. Mix with your hands, adding warm water 2 to 3 Tbs. at a time, until the dough is cohesive; you may need as much as 2/3 cup. The dough should be soft but not sticky.

Shape the gnocchi

• Line 2 rimmed baking sheets with parchment and dust well with flour. Lightly flour a work surface. Turn the dough out onto the flour and gently flatten it by hand or by lightly rolling with a rolling pin until about 3/4 inch thick. If the dough is sticky, lightly dust the top with flour, too.
• With a floured bench scraper or a knife, cut the dough into strips from 1/2 to 3/4 inch wide. With your hands, roll and lengthen the strips until about 1/2 inch in diameter. Using the bench scraper, cut the logs into 1/2- to 1-inch pieces (size is up to you).
• If you want to give the gnocchi ridges, use the side of your thumb to gently roll each piece down the length of a gnocchi board or the tines of a fork, while simultaneously pressing lightly on the dough. (A fork will produce gnocchi with more pronounced ridges than a gnocchi board.)
• Arrange the gnocchi in a single layer on the prepared baking sheets, making sure they don’t touch. If not cooking the gnocchi right away, cover with plastic wrap and refrigerate for up to 4 hours. Even better, freeze the gnocchi right on the baking sheet until hard. (Frozen gnocchi are easier to handle than fresh and hold their shape better.)

Make the sauce

• Combine the cream and cheeses in a medium saucepan, and bring to a simmer, stirring, over medium heat. Cook, whisking occasionally, until the sauce is smooth and thick enough to coat the whisk, 7 to 10 minutes. Add the nutmeg, season to taste with salt, and keep warm.

Cook and serve the gnocchi

• Bring a large pot of well-salted water to a boil. reduce the heat to just below the boil. Add the gnocchi and cook, stirring once, until they float to the surface, 1 to 3 minutes, and then continue to simmer until tender (taste one and see), another 3 to 4 minutes. (The chestnut flour requires more cooking time than all-purpose flour.) Use a slotted spoon or similar utensil to transfer them to a bowl as they cook. Gently toss with enough sauce to coat, and serve immediately.