Preheat the slow cooker if necessary; see the manufacturer's instructions. Heat the oil in a frying pan, add the onions and fry, stirring, for 5 minutes or until just beginning to soften and turn golden.
Stir in the beetroot and cook for 3 minutes, then add the apple, ginger, vinegar and honey. Pour in the stock, add a little salt and pepper and bring to the boil. Pour the mixture into the slow cooker pot, press the beetroot below the surface of the liquid then cover and cook on low for 6–8 hours until tender.
Serve hot as a starter topped with spoonfuls of soured cream and chopped dill or as a vegetable side dish with roast pork or beef or cold with cold sliced meats.