To make Balsamic Vinaigrette: In small bowl, whisk together oil, vinegar, garlic, salt and pepper; set aside. (Make-ahead: Refrigerate in airtight container for up to 1 week.)
Drain tofu on paper towels; cut in half lengthwise and set aside.
Trim stems from mushrooms; place caps in large bowl. Trim green onions to 8-inch (20 cm) lengths; add to bowl. Cut zucchini in half lengthwise; add to bowl. Seed, core and cut red and yellow peppers into quarters; add to bowl.
In small bowl, whisk together oil, basil, salt and pepper; brush 1 tbsp (15 mL) over tofu. Add remainder to vegetables; toss to coat.
Place zucchini, yellow peppers, green onions and tofu on greased grill over medium-high heat; close lid and grill for 5 minutes. Turn vegetables and tofu. Add mushrooms; close lid and grill, turning mushrooms once, until vegetables are tender-crisp and tofu and mushrooms are browned, about 5 minutes longer.
Cut tofu into bite-size pieces; place on large platter. Cut zucchini diagonally into 1/2-inch (1 cm) thick slices; add to platter. Thinly slice mushrooms; add to platter. Arrange green onions and yellow peppers alongside. Drizzle with vinaigrette.