Place a grill pan over medium-high heat or prepare the barbecue (medium-high heat). Brush the vegetables with 1/4 cup of the oil to coat lightly. Sprinkle the vegetables with salt and pepper. Working in batches, grill the vegetables until tender and lightly charred all over, about 8 to 10 minutes for the bell peppers; 7 minutes for the yellow squash, zucchini, eggplant, and mushrooms; 4 minutes for the asparagus and green onions. Arrange the vegetables on a platter. The key to getting those great grill marks is to not shift the vegetables too frequently once they've been placed on the hot grill.
Meanwhile, whisk the remaining 2 tablespoons of oil, balsamic vinegar, garlic, parsley, basil, and rosemary in a small bowl to blend. Add salt and pepper to taste. Drizzle the herb mixture over the vegetables. Serve the vegetables, warm or at room temperature.
Recipe courtesy of Giada De Laurentiis