Place first 6 ingredients cut sides up on baking sheet. Spritz with water. Season with salt and pepper. Let vegetables stand approximately 1 1/2 hours.
Preheat barbecue (medium-high heat). Combine 3 garlic cloves with 1/4 cup vinegar. Drizzle over vegetables. Grill vegetables until tender, turning once. Transfer to baking sheet as each vegetable is tender. Let cool. Reserve all vegetable juices.
Combine remaining 2 garlic cloves and 5 tablespoons vinegar with broth, basil and oil. Coarsely chop vegetables. Place in large bowl. Pour accumulated juices into vinegar mixture. Add lettuce and cheese to vegetables. Pour vinegar mixture over. Toss well. Season with salt and pepper; serve.
Per serving: calories, 160; fat, 6 g; sodium, 120 mg; cholesterol, 4 mg Nutritional analysis provided by Bon Appétit