In the same skillet, caramelize the onions in the butter. Add the honey and cook for 1 minute. Add the balsamic vinegar and reduce until syrupy. Add the broth mixture and mustard and bring to a boil, stirring constantly. Return the patties to the skillet and simmer gently, spooning the sauce over the meat until it is thoroughly cooked. Add broth, as needed. Adjust the seasoning. Sprinkle with the parsley.
