Season the Chicken In a medium bowl, toss the thinly sliced chicken with the Worcestershire sauce, 1 teaspoon of olive oil, 1/2 teaspoon of salt, and 1/4 teaspoon of black pepper. Set aside to marinate for a few minutes while you prep the vegetables.
Sauté the Veggies Heat a large skillet over medium-high heat. Melt the butter with the remaining 1 teaspoon of olive oil. Add the sliced onions and bell peppers along with a pinch of salt. Sauté, stirring occasionally, until the veggies are tender and caramelized around the edges (about 6 to 8 minutes). Stir in the minced garlic and Italian seasoning (if using) and cook for 30 seconds until fragrant. Transfer the vegetables to a plate.
Sear the Chicken Turn the skillet up to high heat. Add a tiny splash of oil if the pan looks dry. Spread the chicken out in an even layer. Let it sear undisturbed for 1 to 2 minutes to get a nice brown crust, then stir and cook for another 3 minutes until fully cooked through. Season with the remaining salt and pepper to taste.
Melt the Cheese Reduce the heat to medium-low. Return the cooked peppers and onions to the skillet, tossing everything together with the chicken. Divide the mixture into 4 even, roll-sized mounds right in the pan. Top each mound with 1 to 2 slices of provolone cheese. Place a lid or a sheet of aluminum foil over the skillet for 30 to 60 seconds to trap the heat and melt the cheese.
Assemble Using a wide spatula, scoop up each cheesy chicken mound and slide it directly into your split hoagie rolls. Serve hot immediately!