Preheat oven to 425°F. Toss mushrooms and zucchini with 2 tablespoons olive oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Spread on baking sheets and roast for 25 minutes until caramelized. Reduce oven to 375°F.
In a large bowl, combine ricotta, cream cheese, eggs, basil, 2 cups mozzarella, 1/2 cup Parmesan, remaining salt and pepper. Mix until smooth.
Heat remaining olive oil in a skillet and sauté garlic for 1 minute. Add marinara sauce and simmer for 5 minutes.
Spread 1 cup sauce in a 9x13 inch baking dish. Layer 4 noodles, half the ricotta mixture, half the roasted vegetables, 1 1/2 cups sauce, and 1 cup mozzarella. Repeat layers once.
Top with remaining 4 noodles, remaining sauce, remaining mozzarella, and remaining Parmesan.
Cover with foil and bake for 45 minutes. Remove foil and bake 15 minutes more until bubbly and golden.
Let rest for 15 minutes before slicing and serving.