Adjust oven racks to upper-middle and lower-middle positions and heat oven to 400 degrees. Toss zucchini and eggplant with 3 tablespoons olive oil, two-thirds of garlic, 1 teaspoon salt, and 1 teaspoon pepper. Spread vegetables in 2 greased rimmed baking sheets and bake, stirring occasionally, until softened and golden brown, for 35 to 45 minutes; set aside.

Heat remaining 2 tablespoons oil in large saucepan over medium heat until shimmering. Add onion and cook until softened, about 5 minutes. Stir in remaining garlic and cook until

fragrant, about 30 seconds. Stir in crushed tomatoes and diced tomatoes with their juice, bring to simmer, and cook until favors meld, for about 5 minutes. Remove from heat, stir in basil and season with salt and pepper to taste. (You should have about 7 cups sauce.)

Spread 1 cup sauce over bottom of 13 by 9-inch baking dish. Lay 3 noodles in dish, spread one-quarter of vegetables over noodles, then top with 1 cup sauce, 2⁄3 cup mozzarella, and 1⁄2 cup Parmesan (in that order). Repeat layering process 2 more times. Top with remaining 3 noodles, remaining vegetables, remaining sauce, remaining 1 cup mozzarella, and remaining 1⁄2 cup Parmesan.

Cover dish tightly with greased aluminum foil, place on foil lined rimmed baking sheet, and bake for 15 minutes. Uncover, and continue to bake until spotty brown and bubbling around edges, for about 30 to 35 minutes. Let lasagna cool for 10 minutes before serving.