Heat oil and butter in a large saut pan. Dredge chicken in seasoned flour and shake off excess. Add to pan and cook until browned, removing to an oven safe platter.
In the same skillet add sliced tomatoes that have been seasoned with salt and pepper and heat through until just beginning to soften but still holding their shape. Remove tomatoes and place on top of chicken. Add garlic and green onions to pan that tomatoes were cooked in. Cook until just soft, about 30 seconds. Add chicken broth and stir, reducing slightly. Then add balsamic vinegar, basil and oregano. Stir gently and pour sauce over the chicken and tomatoes.
Place mozzarella cheese on top of tomatoes and sprinkle with Italian seasoning. Broil until brown and bubbly. Serve hot.
