Put the cabbage in a large bowl. Cover with boiling water and set aside.
Using a large heavy-based pan, either sauté the pork until the fat runs or melt the butter. Add the onions and fry, stirring frequently, over a moderate heat until soft and transparent. Stir in the sugar and continue to fry gently until the onions are caramelized and a rich golden colour. Take great care not to let the sugar burn.
Drain the cabbage thoroughly. Add it to the pan with the apples, stock, wine and vinegar. Mix well. Season generously with salt and pepper. Cover tightly and cook gently for 1½ hours, stirring occasionally.
Mix in the grated beetroot – this transforms the colour – and continue to cook, covered, for 30 minutes longer, or until the cabbage is soft. Adjust the seasoning, if necessary, and serve very hot.