Preheat a grill to high. Grill the rolls until lightly toasted.
Brush the mushroom caps and onion with the olive oil; season with salt and pepper. Place on the grill, cover and cook, turning once, for 8 minutes. Transfer the onion to a plate. Divide the blue cheese among 6 of the mushroom caps, stem side up, and top each with a remaining mushroom, stem side down. Cover and grill until the cheese melts, about 1 minute. Place a mushroom stack on each of the roll bottoms and top with the onion and roll tops.