Pour 1 cup of balsamic vinegar in small saucepan. Over medium heat simmer vinegar until it's reduced by half. Set aside.
Wash and prepare the vegetables. In a large bowl toss vegetables with 2 tablespoons of extra virgin olive oil. Heat a grill pan or grill on high heat. Brush olive oil on the grill pan when hot and add the carrots, peppers and onion. Grill on the first side for approx. 5 minutes to get grill marks. Continue to turn as needed. When the vegetables are almost cooked through (about 10 minutes) add the asparagus, zucchini and mushrooms. Continue to grill until all vegetable are cooked through.
Arrange the cooked vegetables on a large serving platter. Drizzle with the reduced balsamic vinegar and remaining 2 tablespoons of extra virgin olive oil. Sprinkle with the coarse sea salt and pepper. Serve hot.