Place the mushrooms gill side up on the hot grill over direct heat. Place the pepper rings along the edges of the grill over indirect heat. Grill the mushrooms until tender and juicy, about 12 to 15 minutes, then flip, draining any juices, and grill an additional 2 minutes. If desired, flip one more time and melt sliced cheese onto the mushrooms. Meanwhile, cook the peppers until tender, about 15 minutes. If desired, place the peppers over direct heat toward the end of the cooking time to blacken them.