In a saucepan, boil the wine until reduced by half. Add the vegetable broth and the beef stock to the pan. Finely chop the gingerbread, add to the pan and bring to the boil. Remove from the heat, cover and let stand 5 minutes. Puree with an immersion blender, season with salt and pepper and if necessary, add a little vinegar. Return to a simmer.
Season the beef fillet with salt and pepper, place it in the hot, simmering (not boiling) sauce and cook 6 minutes.
Remove the stalk from the cabbage and cut the cabbage into thin strips. Rinse and drain.
Heat the butter in a skillet and saute the cabbage over medium heat, stirring frequently until crisp, season with salt and pepper. To serve, divide the cabbage among plates, top with the beef, stir the sauce and spoon over the meat. If desired, serve with potato dumplings.