In a medium pot or Dutch oven, cook the onions in the butter over medium heat until softened, about 5 minutes. Add the cabbage and cook, stirring, for a few minutes. Add the apple, brown sugar, wine, vinegar, and water, and bring up to a simmer, stirring. Cover and braise for 30 minutes, stirring once and checking on the texture. Cook a little less for a firmer cabbage; a little more for softer cabbage.
Add a small splash of cider vinegar just before serving.