Slice each hoagie roll in half and spread butter on the cut sides.
Heat a large skillet over medium heat and place the rolls cut-side down; toast until lightly browned, 1–3 minutes, then remove and set aside.
If using, mix 1 tablespoon mayonnaise with 1/4 teaspoon garlic powder and spread on the inside of each toasted roll.
Add 1 tablespoon vegetable oil to the skillet and increase heat to medium-high.
Thinly slice the chicken breasts and season evenly with 1 teaspoon garlic powder, 1/2 teaspoon salt, and 1/2 teaspoon black pepper.
Add the sliced chicken to the hot skillet in a single layer and sear 2–3 minutes on the first side, then flip and cook 1–3 more minutes until no longer pink; remove chicken and set aside.
Add the thinly sliced onion and green bell pepper to the skillet and cook 2–3 minutes without stirring to sear, then stir and continue cooking 1–3 minutes until softened.
Return the cooked chicken to the skillet with the peppers and onions, reduce heat to low, then arrange the provolone slices over the mixture and cover with a lid or foil until the cheese melts, about 1–3 minutes.
Use a spatula to divide the cheesy chicken and vegetable mixture among the toasted rolls and serve immediately.