Hearty Vegetable Lasagna

1. FOR THE TOMATO SAUCE: Whisk all ingredients together in bowl; set aside.
2. FOR THE CREAM SAUCE: Whisk all ingredients together in separate bowl; set aside.
3. FOR THE FILLING: Adjust oven rack to middle position and heat oven to 375 degrees. Toss eggplant with 1 teaspoon salt in large bowl. Line surface of large plate with double layer of coffee filters and lightly spray with vegetable oil spray. Spread eggplant in even layer over coffee filters; wipe out and reserve bowl. Microwave eggplant, uncovered, until dry to touch and slightly shriveled, about 10 minutes, tossing halfway through cooking. Cool slightly. Return eggplant to bowl and toss with zucchini and summer squash.
4. Combine 1 tablespoon oil, garlic, and thyme in small bowl. Heat 2 tablespoons oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add half of eggplant mixture, 1⁄4 teaspoon salt, and 1⁄4 teaspoon pepper and cook, stirring occasionally, until vegetables are lightly browned, about 7 minutes. Clear center of skillet, add half of garlic mixture, and cook, mashing with spatula, until fragrant, about 30 seconds. Stir garlic mixture into vegetables and transfer to medium bowl. Repeat with remaining eggplant mixture, 2 tablespoons oil, and remaining garlic mixture; transfer to bowl.
5. Heat remaining 1 teaspoon oil in now-empty skillet over medium-high heat until shimmering. Add spinach and cook, stirring frequently, until wilted, about 3 minutes. Transfer spinach to paper towel–lined plate and drain for 2 minutes. Stir into eggplant mixture.
6. Grease 13 by 9-inch baking dish. Spread 1 cup tomato sauce evenly over bottom of dish. Arrange 4 noodles on top of sauce (noodles will overlap). Spread half of vegetable mixture over noodles, followed by half of olives. Spoon half of cream sauce over top and sprinkle with 1 cup mozzarella. Repeat layering with 4 noodles, 1 cup tomato sauce, remaining vegetables, remaining olives, remaining cream sauce and 1 cup more mozzarella. For final layer, arrange remaining 4 noodles on top and cover completely with remaining tomato sauce. Sprinkle with remaining 1 cup mozzarella.
7. Cover dish tightly with aluminum foil that has been sprayed with oil spray and bake until edges are just bubbling, about 35 minutes, rotating dish halfway through baking. Cool lasagna for 25 minutes, then sprinkle with basil and serve.

Part-skim mozzarella can also be used in this recipe, but avoid preshredded cheese, as it does not melt well.