Preheat your oven to 425°F. On two large, rimmed baking sheets, toss the sliced eggplant, zucchini, bell peppers, and onion with 3/4 cup of the pure olive oil, minced garlic, 1 teaspoon of the salt, and 1/2 teaspoon of the black pepper. Spread the vegetables in a single layer. Roast for 25 to 30 minutes, stirring halfway through, until the vegetables are tender and their edges are lightly browned. Remove them from the oven and reduce the oven temperature to 375°F.
While the vegetables roast, make the sauce. In a medium bowl, combine the crushed tomatoes, chopped basil, dried oregano, and the remaining 1 teaspoon of salt and 1/2 teaspoon of black pepper. Stir until well mixed.
In a separate large bowl, make the ricotta filling. Stir together the room-temperature ricotta cheese, beaten eggs, 1/4 cup of the grated Parmesan, and the remaining 1/4 cup of pure olive oil. Mix until smooth and well combined.
Assemble the lasagna in a 9x13-inch baking dish. Spread 1/2 cup of the tomato sauce evenly over the bottom. Arrange 4 no-boil lasagna noodles over the sauce, breaking them to fit if necessary. Spread half of the ricotta mixture over the noodles. Layer half of the roasted vegetables evenly over the ricotta, then sprinkle half of the chopped spinach over the vegetables. Top with 1/3 of the shredded mozzarella cheese.
Repeat the layers: Add another 1/2 cup of sauce, then 4 more noodles. Spread with the remaining ricotta mixture, the remaining roasted vegetables, and the remaining chopped spinach. Top with another 1/3 of the mozzarella. For the final layer, place the last 4 noodles on top. Spread the remaining tomato sauce over the noodles, then sprinkle with the remaining mozzarella and the last 1/4 cup of Parmesan.
Cover the baking dish tightly with aluminum foil. Bake at 375°F for 30 minutes. Then, carefully remove the foil and continue baking for another 15 to 20 minutes, until the cheese is bubbly and the edges are golden brown. Remove the lasagna from the oven and let it rest for 15 minutes to set before slicing and serving.