Heat olive oil in a large skillet over medium-high heat. Add the sliced onions and peppers. Sauté for 5–6 minutes until soft and slightly caramelized. Remove from skillet and set aside.
In the same skillet, add the sliced or shredded chicken. Season lightly with salt and pepper. Cook for 5–7 minutes, stirring occasionally, until fully cooked and lightly browned.
Lower the heat to medium and stir in the buffalo sauce. Add the cooked onions and peppers back into the skillet. Toss everything together until well coated and heated through.
Split the hoagie rolls and optionally butter the insides. Toast them in a pan or oven until golden.
Divide the buffalo chicken mixture among the rolls and top each with 2 slices of cheese. If needed, place under a broiler for 1–2 minutes to melt the cheese.
Drizzle with ranch or blue cheese dressing, if desired, and serve immediately while hot and melty.