Preheat the oven to 375°F (190°C).
Begin by preparing the chicken breasts. Make a horizontal incision along the side of each chicken breast to create a pocket, being careful not to cut all the way through. Season the inside and outside of each breast with garlic powder, dried oregano, salt, and pepper.
Stuff each chicken breast pocket with sliced mushrooms and mozzarella cheese chunks, distributing them evenly.
Secure the openings of the chicken breasts with toothpicks to prevent the filling from falling out during cooking.
Place the stuffed chicken breasts in a baking dish. If desired, pour the optional sauce ingredients (chicken broth, sliced mushrooms, cornstarch dissolved in water, salt, pepper, and vinegar) around the chicken breasts in the baking dish.
Cover the baking dish with aluminum foil and bake in the preheated oven for about 25-30 minutes, or until the chicken is cooked through and no longer pink in the center.
Remove the foil and bake for an additional 10 minutes, or until the chicken is golden brown and the cheese is bubbly and melted.
Once cooked, remove the toothpicks from the chicken breasts and discard.
Serve the stuffed chicken breasts hot, accompanied by the optional sauce if desired.