In a large bowl, toss the thinly sliced chicken with Worcestershire sauce, 1 teaspoon olive oil, 1/2 teaspoon kosher salt, and black pepper until evenly coated.

Heat a large skillet over medium-high heat. Add 1 teaspoon olive oil and the unsalted butter.

Once melted, add the thinly sliced onion and both bell peppers with a pinch of kosher salt. Sauté, stirring frequently, for 6 to 8 minutes until vegetables are tender and beginning to caramelize.

Stir in the minced garlic and Italian seasoning, cooking for 30 seconds until fragrant. Transfer vegetables to a plate and set aside.

If needed, add a touch of olive oil to the skillet. Increase heat to high.

Arrange the seasoned chicken in an even layer and sear for 1 to 2 minutes without moving, then continue cooking for an additional 3 to 4 minutes, stirring occasionally, until browned and cooked through.

Season with additional kosher salt and pepper to taste.

Return the sautéed onions and peppers to the skillet. Reduce heat to medium-low and combine with the chicken.

Divide the mixture into four even portions and top each with 1 to 2 slices of provolone or white American cheese. Cover the skillet and let the cheese melt, about 30 to 60 seconds.

If desired, spread each hoagie roll with garlic-herb mayonnaise, Dijon, or butter. Fill each roll with a cheesy chicken and vegetable portion. Serve immediately while hot.