Vegetables taste best when cooked on the grill! With this recipe, make the marinade ahead of time; freeze it and stash it in your cooler to help keep everything else cold.
Clean, trim, and peel vegetables. Slice larger ones (such as squash and eggplant), into ¼-inch-thick pieces. You can grill many vegetables whole, or cut them into wide strips or slices for skewering. Skewer small vegetables and onions. Place vegetables in two extra-large resealable plastic bags. Combine remaining ingredients and divide between the two bags. Refrigerate until ready to use.
Preheat grill to medium-low heat. Remove vegetables from bags, and shake off excess marinade. Place vegetables on grill, staggering them by size and density. Grill carrots, fennel, peppers, and onions for 20 to 25 minutes. Grill eggplant slices for 10 minutes. Grill summer squash and portobello mushrooms for 5 to 7 minutes. Turn vegetables part way through their grilling time for consistent cooking. The vegetables should be tender, but not burned. Arrange grilled vegetables on a large platter to make a colorful side dish.