1Heat gas or charcoal grill. In 1-quart saucepan, heat 1/4 cup water to boiling. Add asparagus. Cover; cook 4 minutes or until crisp-tender, adding corn during last 2 minutes of cooking time. Drain.
2In medium bowl, mix asparagus, corn, bread crumbs, cheese, chives, broth, 1/4 teaspoon of the salt and the pepper. Set aside.
3Brush mushroom caps with oil; sprinkle with remaining 1/4 teaspoon salt. Place mushrooms, gill sides down, on grill over medium heat. Cover grill; cook 5 minutes. Turn mushrooms over; mound about 1/2 cup vegetable mixture into each mushroom. Cover grill; cook 5 to 7 minutes longer or until stuffing is golden brown and cheese is melted.