Preheat oven to 375°F. Cook noodles according to package; drain and lay flat on baking sheet to prevent sticking.
Heat oil in large skillet over medium; cook onion 5 minutes until softened. Add garlic, zucchini, and mushrooms; cook 8-10 minutes until tender and liquid evaporates. Stir in spinach until wilted; season with salt and pepper.
Mix ricotta, egg, 1 cup mozzarella, 1/2 cup Parmesan, nutmeg, and Italian seasoning well in medium bowl.
Spread 1 cup marinara in 9x13 inch dish bottom; layer 4 noodles over sauce.
Spread half the ricotta over noodles; top with half the vegetables, 1/2 cup marinara, and 1/2 cup mozzarella.
Repeat: 4 noodles, remaining ricotta and vegetables, 1/2 cup marinara, and 1/2 cup mozzarella.
Top with final 4 noodles, remaining marinara, remaining 1 cup mozzarella, and remaining 1/2 cup Parmesan.
Cover with foil; bake 30 minutes. Uncover; bake another 15 minutes until cheese is bubbly and golden. Rest 10 minutes before slicing.