Combine the salt, brown sugar, granulated garlic, and thyme in a small bowl. Season the fillets generously with the cure mix and set aside in the refrigerator for one or two hours.
Meanwhile, preheat a smoker to 225°F. Smoke the fillets until they are nicely browned, lightly crisp at the edges and flake easily. This takes about 40-50 minutes.
Mix the cream cheese, horseradish, pickled peppers, onion, celery, and parsley together in a medium bowl. Once the smoked fish is cool enough to handle, crumble it into the bowl and mix to just combine. If you prefer a finer texture, mix the fish more and break it up to your liking.
Serve cold with parsley and celery leaves as garnish with a dusting of paprika on top.