Preheat oven to 375°F.
Arrange eggplant and zucchini on parchment-lined sheet pans.
Brush vegetables with olive oil, and sprinkle with oregano, salt, and pepper.
Roast at 375°F for 25 minutes, then add garlic and roast for 5 more minutes.
Lower oven temperature to 350°F.
Soak noodles in hot water for 15 minutes, and drain.
Mix ricotta, goat cheese, eggs, basil, Parmesan, salt, and pepper.
Layer marinara, vegetables, noodles, mozzarella, ricotta mixture, repeat twice, top with marinara and Parmesan. Bake at 350°F for 60-70 minutes, rest 10 minutes before serving.
