While I think this celery salad is best served right after it is mixed, you could make this ahead of time. Store it in an airtight container for up to 3 days.
Parmigiano-Reggiano is a hard, salty unpasteurized cow's milk cheese exclusively from the Emilia-Romanga region of Italy. The word, Parmesan is often used generically for various simulations of this cheese. You can use Parmigiano-Reggiano, Parmesan or Pecorino Romano interchangeably in this recipe.
If you are allergic to walnuts, raw pumpkin seeds would be a good alternative.