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.
Provolone is one of the traditional cheeses for steak sandwiches, but you can also use mozzarella or Monterey Jack. Hoagie rolls are also sold as sub or hero rolls.