Make the dough
Position a rack in the center of the oven and heat to 350°F.
Put the beets in a baking dish, season lightly with salt and pepper, drizzle with the oil, and add 1/4 cup water to the dish. Cover with foil and roast until easily pierced with a skewer, 45 to 60 minutes. (Alternatively, roast the beets in a heavy-duty foil packet on a rimmed baking sheet.) When cool enough to handle, peel and cut the beets into chunks.
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.
Combine the beets, egg, and yolk in a blender or food processor and process until smooth. Transfer to the bowl of still-warm potatoes. Add the flour, 1-1/2 tsp. salt, and the nutmeg, and mix gently with your fingers until the dough comes together; it will be sticky. Add more flour, 1 Tbs. at a time, until 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 butter and sage in a medium saucepan. Cook over medium-low heat, stirring occasionally, until the milk solids turn golden brown and smell toasty, about 10 minutes. Remove the sage leaves. (If you like, reserve them to serve over the finished gnocchi; leave small ones whole, but crumble large ones.) Season the sauce lightly with salt, and keep warm.
Cook and serve the gnocchi
Have the sauce ready and warm on the stove. 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. Use a slotted spoon or similar utensil to transfer them to a bowl as they cook.
Gently toss the gnocchi with enough sauce to coat well, garnish with the reserved sage leaves, if you like, and serve immediately.
Make Ahead Tips
You can freeze the shaped, uncooked gnocchi for up to 1 month. Once frozen rock solid on the baking sheets, transfer them to freezer bags and return to the freezer. Cook as directed without thawing.
nutrition information (per serving):
Size : 1 portion of gnocchi plus 1 Tbs. sauce, Calories (kcal): 570, Fat Calories (kcal): 350, Fat (g): 40, Saturated Fat (g): 22, Polyunsaturated Fat (g): 2, Monounsaturated Fat (g): 13, Cholesterol (mg): 150, Sodium (mg): 645, Carbohydrates (g): 46, Fiber (g): 3, Sugar (g): 4, Protein (g): 8