Heat the butter in a saucepan and let the sugar caramelize in it. Deglaze with balsamic vinegar (be careful with the vinegar fumes). Add the apple cubes and walnuts (put a few chopped walnuts aside for decoration). Fry for 2 minutes while stirring.
Put the red cabbage and the broth in the saucepan and cook on a low heat for 15 minutes. Purée finely with a hand blender, pour in the cream and bring to the boil again briefly. Season to taste with salt, pepper and cinnamon and possibly a little vinegar. Serve sprinkled with the remaining walnuts.