Remove the core from the piece of cabbage, then use a very sharp knife or a food processor to shred the cabbage as thinly as possible. Place it in a large bowl.
Add the raisins and cider vinegar to the cabbage. Squeeze in the juice of one of the clementines and add a pinch of salt and a twist of pepper. Tumble everything together and leave to stand for 15–20 minutes. This will slightly soften the cabbage and plump up the raisins.
Grate the carrots coarsely and scatter them over a large serving platter. Give the cabbage and raisins a good stir, pile on top of the carrots, and pour over any juice left in the bowl.
Peel the remaining 3 clementines and use a very sharp knife to slice them into 1cm thick rounds (don’t worry if some of the rounds fall apart). Lay the fruit over the top of the cabbage. Scatter over the chopped walnuts. Finish, if you like, with a trickle of extra virgin olive oil, and serve.
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