Brush both sides of mushrooms evenly with 3 tablespoons Italian dressing. Coat grill rack with cooking spray; place on grill over medium hot coals (350 to 400).
Place mushrooms on rack; grill, covered, 4 minutes on each side or until tender.
Place cheese over mushrooms, and grill 1 additional minute to melt cheese.
Brush buns with remaining 1 tablespoon dressing; grill, covered, until lightly toasted.
Place mushrooms over bottoms of buns; top with roasted pepper pieces and tops of buns.
