To make the dressing, add the chopped shallot to a small bowl or jug. Add the remaining ingredients and whisk to combine. Season with salt and pepper and set aside to infuse. This can be made ahead.
Make the salad just before serving so the vegetables and apple retain their crunch. For extra crispness, soak the fennel in iced water, then drain and towel or spin dry.
In a large bowl, combine the fennel, celery, apple, walnuts, dill, and about two-thirds of the Parmesan. Add most of the dressing and toss well. Add more dressing if needed, or serve the rest on the side. Season to taste.
Transfer the salad to a flat serving platter and decorate with the extra apple slices (if using) and more Parmesan.