Roast the nuts in a pan without fat until golden brown. Clean the white cabbage and cut out the stalk. Slice the cabbage into thin strips on a vegetable slicer. Add salt and 1 tablespoon of oil and work everything through well with your hands.
Clean and peel the carrots and slice them into fine strips on the vegetable slicer. Wash and dry apples. Cut 1 apple into quarters, remove seeds and slice into strips. Add carrots and apple strips to the cabbage. Chop the fennel seed.
Mix apple juice, lemon juice, fennel, salt and pepper. Beat the remaining oil into the mixture. Mix salad and vinaigrette and leave to stand for at least 1 hour. Clean, wash and drain the lamb's lettuce.
Quarter the remaining apple and cut out the core. Cut the quarter into small boats. Arrange salad with apple boats and lamb's lettuce.