Preheat oven to 375. Combine ricotta, egg, nutmeg, and salt in a medium bowl. Season with pepper. Coarsely grate 1/2 of the mozzarella, and stir into ricotta mixture. Using your fingers, shred remaining mozzarella into 2-inch strips, and reserve.
Spread 1/2 cup marinara in a 9-by-13-inch baking dish. Place a layer of noodles over marinara. Spread 1/3 of the ricotta mixture over noodles, and sprinkle with 1/3 of the Parmesan. Place a layer of noodles over the cheese layer. Spread 1 cup marinara over noodles. Repeat layering (noodles, marinara, noodles, ricotta mixture, Parmesan) 2 more times. Spread remaining marinara over cheese layer, then sprinkle with shredded mozzarella.
Place baking dish on a rimmed baking sheet. Bake until cheese is golden brown and sauce is bubbling, 45 to 50 minutes. Let stand for 15 minutes before slicing and serving.