Bring vinegar to a boil in a small saucepan set over medium-low heat. Reduce heat to medium-low and simmer for 10 to 15 minutes, stirring often, until vinegar has reduced and thickened enough that it lightly coats the back of a spoon. Set aside to cool.
Toss bell peppers, zucchini, and mushrooms with oil and salt and pepper to taste.
Place vegetables in a grill basket. Grill over medium heat for approximately 15 minutes, or until veggies are fork tender.
Serve grilled vegetables with a drizzle of balsamic glaze over. Garnish with basil.