Remove stems from mushrooms and clean. Cut peppers in half lengthwise. Remove seeds and flatten peppers with the palm of your hand. Cut squash lengthwise into 1/2 inch thick slices. Cut tomato crosswise into 1/2 inch thick slices. Place vegetables in large plastic zipper bag. In small bowl, whisk together olive oil, rosemary, shallot, salt, and pepper. Add mixture to veggies and marinate at room temperature for 15-30 minutes.
Remove veggies from bag, and place on grill over medium heat. Cook, turning once, until tender. Transfer to a large platter, and drizzle with balsamic vinegar. Toast the bread slices on the grill, and then evenly spread goat cheese onto bread. Build the sandwiches with the grilled veggies, interspersing the sliced basil leaves. Top with remaining bread slices. 4 servings.