Preheat the Blackstone grill over medium high heat (approximately 400 degrees F).
Add the oil and butter to the middle of the grill. Spread it around so that it can melt.
Add the peppers and onions to the grill. Toss them to coat them in the oil and butter. Sauté for 3-5 minutes until peppers are cooked to your preference.
Move the peppers and onions to a cooler part of the grill (front or a part of the grill where the burner is off or remove from grill and set aside).
Place your hoagie rolls rolls face down on the cooler side of the grill as well so that they will toast slightly. Watch closely so that the rolls do not burn.
Add the chicken to the center of the grill. Spread it out to a thin layer. Season with the Italian seasoning, salt and pepper. Let the chicken sear for 3-5 minutes until the juices start to flow. Flip and then use your spatula to chop into smaller pieces. Continue cooking the chicken until is cooked through (2-3 more minutes).
Then divide into 4 equal piles on the grill and top each pile with the pepper and onion mixture. Immediately top each pile with 2 slices of cheese and let the cheese melt (1-2 minutes).
Use your spatula to scoop and lift each pile and place the mixture onto one of the toasted hoagie rolls.
Serve immediately while warm and enjoy!