Coarsely chop the walnuts and roast them briefly in a pan without fat, remove them. For the vinaigrette, whisk vinegar, salt, pepper and honey. Add oil drop by drop. Peel shallot and cut into fine cubes.
Stir the nuts and shallot into the vinaigrette. Clean the salad, wash and spin dry. Wash and halve the tomatoes. Arrange lettuce and tomatoes on plates and sprinkle with vinaigrette. Sprinkle with parmesan slices.