Preheat oven to 400°F (200°C). In a large mixing bowl, combine the cubed eggplant, zucchini, halved cherry tomatoes, and chopped red onion. Add olive oil, minced garlic, dried oregano, dried basil, red pepper flakes (if using), 1 teaspoon salt, and 1/2 teaspoon black pepper. Toss well to ensure all vegetables are evenly coated.

Spread the seasoned vegetables in a single layer on a large baking sheet. Roast for 15-20 minutes, stirring halfway through, until the vegetables are slightly tender and lightly browned. This step concentrates their flavor and removes excess moisture.

While vegetables are roasting, lightly grease a 9x13 inch baking dish (or similar size).

In a large bowl, combine the roasted vegetables with the crushed tomatoes and 1/4 cup of the chopped fresh basil. Stir gently to mix. Pour half of the vegetable mixture into the prepared baking dish. Sprinkle with half of the grated Parmesan cheese.

Spoon the remaining vegetable mixture over the Parmesan layer. Top evenly with the shredded mozzarella cheese and the remaining 1/4 cup of Parmesan cheese.

Place the baking dish in the preheated oven. Bake for 25-30 minutes, or until the cheese is melted, bubbly, and lightly golden brown, and the sauce is simmering.

Remove from oven and let stand for 5-10 minutes before serving. Garnish with extra fresh basil, if desired. Serve hot as a main course with crusty bread or as a side dish.