In a large 12" sauté pan over medium heat, cook onions and garlic in a little butter until lightly golden and tender, about 5 minutes.
As onions are cooking, cook pasta per package directions in boiling, salted water until just done (for me, this was about 8-9 minutes of cook time.) Drain but don't rinse pasta.
Add cream, 1 cup parmesan cheese, and nutmeg. Season with salt and pepper, and reduce heat to medium-low. Cook until cream reduces and sauce is thickened, about 20 minutes.
Add pasta and spinach to pan, stir, and cover until spinach has wilted slightly, about 3 minutes.
Add mozzarella, then transfer the mixture to an oven-safe baking dish and top with remaining 1/2 cup each mozzarella and Parmesan.