Put the ricotta, Parmigiano-Reggiano, nutmeg, pepper, egg yolk, 1/2 teaspoon salt and 1/2 cup of the flour in a large bowl. Use a wooden spoon to mix until a shaggy dough forms. Do not overwork. Continue to mix until the dough comes together and forms a ball, adding an additional 1/4 cup flour if needed.
Lightly flour your hands and roll the mixture into quarter-sized balls; there should be 25 to 30 balls. Place the gnudi onto a lightly floured tray and refrigerate for at least 30 minutes and up to 1 hour.
Meanwhile, add the oil, capers and sage leaves to a small saute pan. Place over medium heat and fry until crispy, 6 to 8 minutes. If the sage leaves become too dark, remove them before the capers. Transfer to a plate lined with paper towels. Set aside.
Bring a large pot of salted water to a low boil.
Add the butter and sage sprig to a large saute pan over medium-high heat. Melt the butter and continue to cook, swirling the pan in a circular motion to prevent the butter from burning, until it starts to turn golden brown and begins to smell nutty. Squeeze the juice from a lemon wedge into the pan to stop the butter from turning too dark and burning.
Once the water is at a low boil, add the gnudi and cook until they float, 2 to 3 minutes. Using a slotted spoon, remove the gnudi directly into the browned butter. Stir to coat.
Plate the gnudi onto a serving plate and garnish with the fried sage and capers and additional Parmigiano-Reggiano. Serve with lemon wedges.