How to Make It
Preheat the oven to 375º. In a 9-inch square baking dish, brush the beets with olive oil and season with salt and pepper. Add 1/4 cup of water to the baking dish and cover tightly with foil. Bake the beets for about 1 hour, until tender. Uncover the dish and let the beets cool completely.
Peel the beets and cut them into 1-inch pieces. Transfer the beets to a food processor and puree.
In the bowl of a standing mixer fitted with the paddle, combine 1 1/2 cups of the beet puree (reserve any remaining puree for another use) with the ricotta, egg, nutmeg, the 3/4 cup of Parmigiano and 1 tablespoon of salt and mix at low speed until combined. Using a rubber spatula, scrape down the side of the bowl. Sprinkle on the 3 cups of flour and mix at low speed until the dough just comes together, about 1 minute.
Scrape the dough onto a lightly floured work surface and knead gently just until smooth but still slightly sticky. Cover the dough with plastic wrap and let stand at room temperature for 30 minutes.
Line a baking sheet with wax paper and generously dust with flour. Cut the gnocchi dough into 10 pieces and roll each piece into a 1/2-inch-thick rope. Cut the ropes into 1/2-inch pieces and transfer the gnocchi to the prepared baking sheet.
Lightly oil another baking sheet. In a large, deep skillet of simmering salted water, cook one-fourth of the gnocchi until they rise to the surface, then simmer for 1 minute longer, or until they are cooked through. Using a slotted spoon, transfer the gnocchi to the oiled baking sheet. Repeat with the remaining uncooked gnocchi.
In a very large skillet, toast the chopped walnuts over moderate heat, tossing, until golden and fragrant, 3 to 5 minutes. Transfer to a plate and let cool.
Add the butter to the skillet and cook until golden brown, 2 to 3 minutes. Add the sage leaves and cook for 20 seconds, then stir in the lemon juice. Add the gnocchi and cook for 1 minute, tossing gently. Season with salt and transfer the gnocchi to plates. Sprinkle the toasted walnuts on top and serve, passing grated Parmigiano-Reggiano at the table.
The gnocchi can be prepared through Step 5 and frozen on the baking sheet, then transferred to a resealable plastic bag and frozen for up to 1 month. Cook without thawing.