In a medium bowl, combine the thinly sliced chicken with the Buffalo sauce, ensuring that each piece is well coated. Allow it to marinate while you prepare the other ingredients.
In a large skillet over medium heat, add 1 tablespoon of olive oil. Once hot, toss in the sliced onion and green bell pepper. Sauté these veggies for about 4-5 minutes until they are softened and slightly caramelized.
Using the same skillet, add another tablespoon of olive oil and then introduce the marinated chicken slices. Spread them out evenly in a single layer and sauté for about 5-7 minutes until fully cooked and slightly crispy around the edges. Season with salt and pepper to taste.
Preheat your oven to broil. Slice open each hoagie roll and lay them out on a baking sheet. Evenly distribute the cooked chicken among each roll followed by generous portions of sautéed onions and peppers.
Sprinkle shredded mozzarella cheese over each loaded hoagie roll and place the baking sheet under your broiler for just 1-2 minutes until the cheese melts.
Drizzle some extra Buffalo sauce over each cheesesteak if desired. Garnish with chopped parsley before serving.