Cut the chicory heads in half lengthwise and remove the hard core at the bottom with a pointed knife. This core contains most of the bitter compounds; if you leave it in, the bitterness will overpower everything else you add. Then slice the halves diagonally into wide strips.
Cut the unpeeled apple into thin matchsticks and toss them immediately with a splash of lemon juice to prevent them from browning. Slice the celery into paper-thin crescents.
Dry-toast the walnuts in a frying pan over medium-high heat until fragrant, about four minutes. Shake the pan regularly, as high-fat nuts quickly go from toasted to bitter. Let them cool and break them up coarsely.
Whisk the yogurt with the mayonnaise, mustard, some lemon zest, the juice of half a lemon, salt, and black pepper into a smooth, thick dressing. The yogurt keeps it fresh and light, while the tablespoon of mayonnaise provides enough fat to help the dressing cling to the leaves.
Remove the skin from the smoked mackerel and flake the flesh into large pieces. Remove the backbone and the dark lateral parts.
Toss the chicory, apple, and celery with the olive oil and two-thirds of the dressing. Gently fold in the mackerel so the flakes remain intact.
Finish with the walnuts, the remaining dressing, plenty of dill and parsley, and black pepper.