Heat broiler, with rack set 4 inches from heat. On a rimmed baking sheet lined with aluminum foil, toss chicken with 1 tablespoon oil; season with salt and pepper. Broil, without turning, until chicken is opaque throughout, 5 to 7 minutes. Transfer to a cutting board (reserve baking sheet); let cool, and thinly slice. Set chicken aside. On baking sheet, toss together peppers, onion, garlic, and remaining tablespoon oil. Broil, tossing occasionally, until crisp-tender and slightly charred, 8 to 10 minutes; season with salt and pepper. Add chicken to broiled vegetables; toss, and spread in a single layer. Top chicken and vegetables with cheese; broil until cheese is bubbling, 30 seconds to 1 minute. Scoop out most of the doughy center from both halves of rolls; discard. Spread rolls with mayonnaise; fill with chicken and vegetables. Serve immediately.