Heat gas or charcoal grill. In 8-inch (2-quart) glass baking dish, mix zucchini, bell pepper and onion. Drizzle with oil; toss to coat. With tongs, place vegetables in grill basket (grill "wok").
When grill is heated, place grill basket on gas grill over medium heat or on charcoal grill over medium coals; cover grill. Cook 15 to 20 minutes, stirring occasionally, until vegetables are crisp-tender. Remove grill basket from grill; place vegetables in 8-inch dish. Stir in oregano and garlic.
Cut 18x18-inch sheet of heavy-duty foil; lightly spray foil with cooking spray. Cut loaf of bread in half lengthwise. Spread cut sides of bread with dressing.
Top bottom half with grilled vegetable mixture. Place cheese slices diagonally over vegetables, overlapping slightly. Cover with top half of bread. Place on foil; wrap securely using double-fold seals, allowing room for heat expansion.
Reduce gas grill to low heat or adjust coals for low heat. Place wrapped loaf on grill; cover grill. Cook 7 to 10 minutes or until warm. Carefully unwrap loaf to allow steam to escape. Cut loaf into 4 sandwiches.