Slice the cabbage very thin.
Warm the oil in a medium saucepan over medium heat. Add the onions and saute for 7 minutes or until the onions are softened.
Add the caraway and cook for 2-3 minutes more. Add the cabbage, beer and apple juice, cover and bring to a boil. Reduce the heat to a simmer, and cook for 5 minutes, covered. Uncover and simmer, stirring occasionally, for 15 more minutes, or until the cabbage is tender and the braising liquid has reduced by half.
Add the mustard, umeboshi vinegar, salt and pepper. Cook for 5 minutes more, stirring occasionally. Serve hot.