Heat a very large heavy-based pan. Add the butter and once it has melted, tip in the red cabbage and onions. Sauté over a medium to high heat for about 10 minutes until just beginning to soften.
Stir the apple into the cabbage mixture and then add the pomegranate or cranberry juice, balsamic vinegar, sugar and spices. Bring to the boil, stirring occasionally, then reduce the heat and simmer for about 1 hour over a low heat, stirring every 20 minutes until the cabbage is meltingly tender. Transfer to a warmed dish and serve at once.