Heat oven to 350°F. Heat 2 tablespoons of the oil in Dutch oven over medium heat until hot. Add onions; cook and stir 3 minutes. Add garlic; cook and stir 1 to 2 minutes or until tender. Add mushrooms; cook 3 to 5 minutes or until tender, stirring frequently. Remove vegetables from Dutch oven; set aside.
Heat remaining 2 tablespoons oil in same Dutch oven over medium heat until hot. Add eggplants and zucchini; cook 6 to 8 minutes or until tender, stirring occasionally. Add basil, salt, thyme and pepper; mix well. Stir in tomatoes. Return onion and mushroom mixture to Dutch oven; mix well. Cover.
Bake at 350°F. for 45 minutes. Uncover Dutch oven; bake an additional 45 minutes or until vegetables are very tender. If desired, garnish with shredded fresh Parmesan cheese.