In large skillet, heat 2 tablespoons olive oil over medium heat and cook onion, green peppers, mushrooms and garlic, stirring occasionally, 10 minutes or until vegetables are tender. Remove vegetables and set aside.
In same skillet, heat remaining 4 tablespoons oil and cook zucchini and eggplant, stirring occasionally, 5 minutes or until tender. Return vegetables to skillet. Stir in basil and sauce. Simmer, stirring occasionally, 5 minutes or until heated through. Sprinkle with cheese.