If using an outdoor gas grill: Heat the grill on high. Once high, wipe down the grill and turn the grill down to medium heat. Place the asparagus on one side of the grill and the mushrooms, gill sides up, on the grill. After 3 minutes, roll the asparagus over so that the other side gets some grill marks. After 2 more minutes, take the asparagus off the grill and flip the mushrooms over. Cook the mushrooms, gill side down, for another 3-5 minutes, until they are cooked through.