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