Prepare the Vegetables: Preheat the oven to 375°F. Arrange the eggplant and zucchini in single layers on parchment-lined baking sheets. Brush with olive oil and season with oregano, salt, and pepper. Roast for 25 minutes, sprinkle with garlic, and roast for another 5 minutes.
Mix the Cheese Filling: In a mixing bowl, combine ricotta, goat cheese, eggs, basil, ½ cup Parmesan, salt, and pepper. Mix until smooth.
Assemble the Lasagna: Lower the oven temperature to 350°F. Spread 1 cup marinara sauce in a 9x13-inch baking dish. Layer a third of the roasted vegetables, followed by noodles, mozzarella, and dollops of the ricotta mixture. Repeat twice, ending with marinara and Parmesan on top.
Bake: Cover the dish with foil and bake for 30 minutes. Remove the foil and bake for an additional 30-35 minutes, until bubbly and golden. Let rest for 10 minutes before serving.