1. Preheat grill to high heat.
2. Remove brown gills from undersides of mushrooms with a spoon; discard. Combine mushrooms, garlic, bell pepper, zucchini, onion, and oil in a bowl; toss to coat. Sprinkle with salt and pepper. Arrange vegetables on grill rack coated with cooking spray; grill 8 minutes or just until tender. Slice mushrooms.
3. Roll dough into a 12-inch oval on a lightly floured surface. Place dough on grill rack; grill 2 minutes on each side or until lightly browned.
4. Sprinkle cheese over dough, leaving a 1/2-inch border around edges. Arrange vegetable mixture over cheese. Grill pizza 3 minutes or until cheese melts. Sprinkle pizza with basil leaves and red pepper; cut into 8 slices.