Slice each chicken breast in half lengthwise to make six thinner chicken breast cutlets. Sprinkle both sides with salt, black pepper, and onion powder, to season.
Heat 1 tablespoon of olive oil in a large, heavy-bottomed skillet over medium-high heat. Working in batches, sear half of the chicken for approximately 3 minutes on each side, or until golden and nearly cooked through. Remove the chicken and transfer it to a clean plate. Set aside. Repeat with the remaining chicken cutlets, then remove those to the same plate to rest.
Return the skillet to medium heat. Add a couple of tablespoons of water and scrape off any brown bits that may be stuck to the bottom of the skillet. Add the butter, diced onion, rosemary, and garlic cloves. Mix well to combine. Stirring often, cook for approximately 5 minutes, or until the onions have softened.
Add the chicken broth and the sherry vinegar to the skillet and bring to a simmer. Return the chicken back to the skillet, spooning the garlic sherry sauce over the top of each chicken breast. Cover and continue to cook for 5 minutes or so, or until chicken is cooked through. Season with freshly cracked black pepper and salt, to taste.