Toss the pepper and onion slices in a large bowl. In a large measuring cup, fork-stir your sauce using: balsamic vinegar, Worcestershire, olive oil, broth, chopped garlic, and herbs. Pour the sauce over the sliced peppers and onions and toss well to coat.
Place the split chicken breasts in the bottom of a baking pan sprayed with olive oil. Season with sea salt and pepper, to taste. Pour the balsamic pepper mixture over the chicken and arrange them evenly. Use every last drop of sauce.
Loosely cover the pan with a piece of foil and place in the center of a pre-heated oven. Bake for 20 minutes. Spoon the sauce all over the peppers and chicken breasts to keep everything happy and moist, recover it and continue to bake until everything is melt-in-your-mouth tender (depending upon the thickness of the chicken, and the size of your pepper strips, and your particular oven and altitude it could be an additional 10 minutes or 20 minutes).
You want the chicken to be cooked through (no longer pink inside) and the peppers to be limp and soft.
Serve with a side dish of cooked rice or quinoa, brown rice pasta tossed in pesto, or creamy mashed potatoes, and crisp baby greens on the side.