Quarter squash, zucchini, and eggplant lengthwise, and cut in half. Cut tomatoes and onions into thick slices. Quarter peppers. Leave mushrooms whole. Combine marinade. Pour over vegetables. Chill for 2 1/2 hours. Arrange vegetables on a broiler pan and bake at 350 degrees in a preheated oven for 20 minutes.
Recipe courtesy Chris Lilly