Arrange first 5 ingredients in a single layer on a baking sheet. Brush vegetables evenly with oil; sprinkle with salt and pepper. Place eggplant, onion, and peppers in a single layer on grill rack coated with cooking spray. Grill 4 minutes on each side or until charred. Remove from grill. Place peppers in a large zip-top plastic bag; seal. Let stand 10 minutes. Peel peppers, and cut into thin strips. Cut eggplant into 1/2-inch pieces.
Arrange tomatoes, skin side down, on a grill rack coated with cooking spray. Grill 2 minutes on each side or until soft. Arrange tomatoes alternately with other vegetables on a serving platter. Combine parsley and garlic; sprinkle evenly over vegetables. Garnish with cheese.