Spoon 6 tablespoons oil into each of 3 small bowls. Add chopped mint to first bowl. Add basil and half of garlic to second bowl, and add dried crushed red pepper and remaining garlic to third bowl. Season each oil with salt and pepper.
Combine zucchini and 2 tablespoons mint marinade in medium bowl; toss to coat. Combine eggplant and 2 tablespoons basil marinade in another bowl; toss to coat. Combine bell peppers and 2 tablespoons crushed-pepper marinade in third bowl; toss to coat. (Can be made 2 hours ahead. Let stand at room temperature, tossing occasionally.)
Prepare barbecue (medium-high heat). Grill vegetables until just charred and tender, turning occasionally, about 5 minutes. Arrange vegetables on platter; sprinkle with salt and pepper. Drizzle each with its marinade. (Can be made 2 hours ahead. Let stand at room temperature.) Add cheese to platter and serve.
