1cup grated Parmesan cheese (about 4 ounces), plus more for serving
Salt and pepper
1/3 to 1/2cup semolina flour, as needed
2cups loosely packed fresh basil
2 garlic cloves
1 teaspoon grated lemon zest
1cup olive oil
Instructions
Heat the oven to 400°F. Scrub the beets; wrap them individually in foil and put them on a baking sheet. Roast until a thin-bladed knife pierces one with little resistance, 45 to 90 minutes (they may cook at different rates; remove each as it is done).
While the beets are roasting, put the pistachios on a rimmed baking sheet and toast in the oven, shaking the pan every few minutes and watching like a hawk, until they are golden and fragrant, 3 to 5 minutes.
When the beets are cool enough to handle, peel them. Cut the beets into chunks and puree in a food processor until completely smooth; transfer to a bowl and wash the food processor.
Combine the breadcrumbs in a bowl with the eggs, ricotta, ¾ cup Parmesan cheese, and 1 cup beet puree. Sprinkle with salt and pepper. Stir the mixture until combined, then let it sit for about 10 minutes. Add semolina flour a little at a time until the mixture wants to stick to your hands but won’t quite; it should feel like fresh play dough. Take care not to overmix. With floured hands, form the dough into tiny balls about 1 inch in diameter and put on a platter in a single layer. Refrigerate for at least 30 minutes and up to overnight, covered.
Bring a large pot of water to a boil and salt it. Combine the basil, pistachios, garlic, lemon zest, a sprinkle of salt, and ½ cup oil in a food processor or blender. Puree, stopping to scrape down the sides of the container if necessary and adding the remaining ½ cup oil gradually. Stir in the remaining ¼ cup Parmesan. Taste and adjust the seasoning.
When the water boils, cook the gnudi, a dozen or so at a time, until they come to the surface, about 3 minutes; remove with a slotted spoon and keep warm. Scoop out a cup of cooking water and use it to thin the pesto; start with just a tablespoon so you don’t overdo it; you’re looking for the pesto to coat the back of a spoon. To serve, spoon some pesto onto the bottom of 4 plates or shallow bowls, top with the gnudi, and sprinkle with more grated (or shaved) Parmesan.