In a large heavy-based saucepan, saute pork until the fat runs, or melt the butter. Add the onions, fry, stirring frequently, until soft and transparent. Stir in the sugar and continue to fry gently until the onions are caramelized and golden. Take care not to let the sugar burn.
Drain the cabbage well. Add it to the pan with the apples, stock, wine and vinegar. Mix well. Season generously with salt and pepper. Cover tightly and cook, covered, for 1 1/2 hours, stirring occasionally. Mix in the grated beetroot - this transforms the colour - and continue to cook, covered for 30 minutes longer, or until cabbage is soft. Serve very hot.