Preheat oven to 375ºF. Heat olive oil and butter in a large skillet over medium-high heat until butter is frothy. Add onion, celery and peppers. Cook 1 to 2 minutes until fragrant.
Add garlic and cook 1 minute more. Add chicken and cook 8 to 10 minutes until meat is browned. Season with salt and pepper.
Add chili powder, dry mustard, paprika, Worcestershire sauce and tomato paste. Stir to combine.
Add balsamic vinegar, tomato sauce and chicken broth. Bring to a boil. Reduce heat and simmer for 15 minutes.
Cut the tops of the bread rolls and hollow out the middle, using your fingers to pull out the excess bread.
Brush the inside of the rolls and the soft side of the tops with melted garlic butter and place on a baking sheet. Bake in the preheated oven for 6 to 7 minutes or until lightly toasted. Note: the tops may toast quicker so check on them after about 4 minutes.
Spoon meat filling into the bread bowls. Sprinkle with cheese and green onions. Place tops on bread bowls and serve immediately.