In a large, heavy skillet, heat a drizzle of oil and a blob of butter over medium-high heat. Add the sausage and cook until it starts to brown.
Add the onion and cook for a few minutes, until it softens. Add the cabbage and apple and cook, stirring often and covering with a lid, until soft. Add the cranberry sauce and balsamic vinegar and continue cooking, stirring often, until thickened and softened.
Season with salt and pepper and serve warm. Serves 4.