Bring 4 quarts of water to a boil in a large pot. Add the pasta and salt, cooking until al dente. Stir the spinach into the boiling pot and cook until wilted, about 30 seconds.

Reserve 1 cup of the cooking water, then drain the pasta and spinach and return them to the pot.

Heat olive oil, garlic, nutmeg, and cayenne in a small saucepan over medium heat until the garlic is fragrant and just beginning to sizzle. Remove from the heat and whisk in the smaller portion of ricotta, heavy cream, lemon zest, lemon juice, and salt until the mixture is completely smooth.

Whisk the remaining ricotta, olive oil, black pepper, and salt in a small bowl until the texture is light and creamy; set this aside for topping.

Pour the warm ricotta-cream sauce and the Parmesan over the cooked pasta. Toss well and let the pasta rest for 2 to 4 minutes, tossing frequently, until the sauce thickens and clings to the noodles. If the pasta seems dry, stir in the reserved cooking water a splash at a time.

Transfer the pasta to a platter or individual bowls and dot evenly with spoonfuls of the seasoned ricotta mixture. Serve warm with extra Parmesan on the side.