Chop the cabbage into 4 quarters, cut out the central core and shred the cabbage quarters. Remove the core of the apple, peel and cut into small pieces.
Place everything together in a large saucepan with about 1-1/4 cups water. Bring to the boil, cover and simmer very gently for about 30 minutes, stirring once or twice.
The cabbage should be tender but not soft and the liquid absorbed so the mixture looks glossy. Serve hot. If making ahead, cool and chill. Reheat thoroughly to serve.