Combine the squash, ricotta, 3/4 cup parmesan, the rosemary and nutmeg in a medium bowl. In another bowl, combine the marinara sauce and basil.
Spread 1/2 cup of the marinara in a large nonstick skillet. Cover with 2 lasagna noodles. Spread half of the ricotta mixture on top of the noodles, then sprinkle with one-third of the mozzarella. Add another layer of noodles, the remaining ricotta mixture, 1 cup marinara and half of the remaining mozzarella. Top with the remaining 2 noodles, then the remaining marinara and mozzarella. Sprinkle with the remaining 1/4 cup parmesan.
Cover and cook over medium-low heat until the pasta is tender and the cheese is melted, about 20 minutes. (Check halfway through: If the edges seem dry, add up to 1/2 cup water.) Let rest 5 minutes before serving.