Brush 1 tablespoon olive oil evenly over both sides of eggplant, onion, and zucchini.
Sprinkle with rosemary, pepper, and salt.
Combine 1 tablespoon oil and vinegar in a bowl.
Brush vinegar mixture over cut sides of bread.
Place onion on grill rack coated with cooking spray, and grill for 6 minutes on each side or until tender.
Remove from grill, and separate into rings. Grill eggplant and zucchini 4 minutes on each side or until tender.
Cut zucchini pieces in half crosswise.
Place bread, cut sides down, on grill rack; grill 2 minutes.
Remove from grill.
Place 1 piece of cheese on bottom halves bread portions; top each serving with 1 eggplant slice, 1 tomato slice, 1 basil leaf, 2 pieces zucchini, one-fourth of onion rings, 1 eggplant slice, 1 tomato slice, 1 basil leaf, 1 piece of cheese, and top half of bread.
Place sandwiches on grill rack; grill 2 minutes, covered, or until cheese melts.