Bring the stock to the boil in a large saucepan. Put the beetroot in the bowl of a food processor and process to a coarse paste. Add the beetroot to the stock and season generously with black pepper and a little salt.
Mix the sauerkraut with the dill. Ladle the beetroot and stock into deep bowls. Divide the sauerkraut between them, then spoon over the soured cream.
Finally grate about a tsp of horseradish ( to taste) over the surface of each bowl of soup.