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Use a vegetable peeler or sharp knife to remove the skin from the halved celeriac. (Rub a little lemon juice over the cut side of the other half before storing it, or it will turn brown.) Cut into thin slices, then cut into long matchstick strips as thin as you can. Do the same with the apple, discarding the core.
Mix together the mayonnaise, mustard, lemon juice and parsley, then toss through the celeriac and apple.