Heat a grill to medium heat and rub the grate with a towel dipped in oil. In a large bowl, add the oil and the vegetables and toss. Season with salt and pepper, to taste.
Grill the vegetables, turning rarely, over medium heat until soft and charred, about 5 minutes for the asparagus, 10 minutes for the onions, 15 minutes for the peppers and mushrooms. Take vegetables off the grill and put in a bowl. Add the pesto sauce to a small bowl and add the grilled mushrooms. Toss to coat the mushrooms with the pesto.
For each burger, spread 1 tablespoon of the mustard on the bottom of the bun, top with 1/4 of the goat cheese, then layer on the mushrooms, onion, bell pepper, and asparagus. Cover with the top of the bun and serve.
Cook's Note: You can also use an indoor grill to grill the vegetables.
Per serving: Calories 499; Total Fat 31.5 grams; Saturated Fat 8 grams; Protein 16 grams; Total Carbohydrate 36 grams; Sugar: 10 grams; Fiber 4.5 grams; Cholesterol 18 milligrams; Sodium 738 milligrams;