Melt the butter in a large saucepan over moderate heat. Add the sugar and stir until it melts.
Add the cabbage and cook, stirring occasionally, for two minutes.
Add the vinegar, water, salt and pepper and bring to a simmer.
Lower the heat and cook, covered, until the cabbage is tender, about two hours. Stir the cabbage occasionally while cooking; if the pan seems dry, add a tablespoon or two of water to prevent burning.
Stir the apples and jelly into the cabbage. Simmer the cabbage, covered, for another hour, until the apples are tender and the flavors meld.
The cabbage can be made up to two days ahead (and tastes even better this way), kept covered in the refrigerator. Reheat the cabbage in a saucepan, covered, over moderately low heat. Taste a piece of cabbage and add more salt, pepper, sugar or vinegar to your taste.