Cut the red cabbage into strips as finely as possible and pour in a tablespoon of olive oil and the juice of half a lemon. Add some salt and knead the cabbage firmly with your hands until soft. Set aside.
Cut the chicken into pieces and fry in sesame oil. Season only with pepper and at the end of the frying time, pour in a splash of soy sauce, the remaining lemon juice and honey. Also add the sesame seeds. Let everything simmer and simmer for a minute. Remove the pan from the heat.
Knead the cabbage some more, drain off any liquid and mix in the pickled ginger. Divide the red cabbage among plates, arrange the chicken on top and pour the remaining sauce over the chicken and cabbage. Top with coarsely chopped peanuts and serve.