This dish can be made in advance and reheated before serving.
Cut cabbage in half lengthwise, remove core, and slice as thinly as possible.
Heat oil in a large saucepan over medium-low heat. Add cabbage, and saute stirring until wilted, about 10 minutes. Add vinegar, honey, and spices. Season well with salt and pepper. Add 3 tablespoons water, and continue cooking cabbage until almost soft, about 1 1/2 hours. (Add more water if needed while cabbage is cooking.)
Cut apple in half lengthwise, remove core, and slice into very thin wedges. Add to cabbage, and continue cooking until cabbage is soft and almost dry, about 20 more minutes.