From the kohlrabi remove the delicate, green leaves and put aside for the garnish.
Peel the kohlrabi, cut into equal pieces and sautée in butter. Add the soup and simmer for 15 minutes.
Wash the radishes and cut into thin slices. Crumble the pumpernickel and roast it in butter crispy. Finely puree the soup with the hand-held blender, stir in the crème fraîche. Season the soup with salt and pepper and purée again.
Serve the soup and sprinkled with pumpernickel, garnish with radish slices and cabbage leaves.