In a medium bowl, mix the ricotta, mascarpone, Parmesan, ½ teaspoon salt, and ¼ teaspoon black pepper until smooth. Set aside.
Bring a large pot of salted water to a boil. Add the pasta and cook according to package directions until al dente. Reserve 1 cup of pasta water, then drain and set aside.
Set a large deep skillet over medium heat and melt the butter. Add the shallot and cook for 2 minutes, stirring frequently until softened. Stir in the garlic and cook for an additional 30 seconds.
Add the spinach in batches, stirring frequently until all the leaves are wilted, about 5 minutes. Season with salt and black pepper.
Pour in the heavy cream and bring to a gentle simmer. Cook for 2 minutes to warm through without boiling, then stir in the nutmeg.
Remove the skillet from the heat. Stir in the ricotta–mascarpone mixture until smooth and well blended.
Add the drained pasta to the sauce and toss gently until coated. Add a splash of reserved pasta water if needed to loosen the sauce.
Adjust seasoning to taste, top with extra Parmesan, and serve hot.