In a medium size fry pan over low heat melt the butter with the olive oil. Add the onion, chicken, garlic poweder or fresh garlic, chicken broth, cherry peppers, cherry pepper juice, salt and pepper to taste. Saute, stirring often and breaking up the chicken as fine as possible until the chicken is cooked and most of the liquid is gone. (You don't want the chicken to dr out!) About 8-10 minutes. Take off the heat, cover and set aside.
Open the roll, butter it and lay the cheese on. Broil the roll or bread until the cheese is mostly melted and the bun is warm, not crunchy.
Spoon on the chicken mixture, sprinkle with lettuce and tomato. Drizzle with a little olive oil and season with salt and pepper. Serve warm.