Combine the curing ingredients - white sugar, brown sugar, Kosher salt, and black pepper - in a medium size bowl and mix together.
Place a sheet of tin foil on top of a long, rimmed baking sheet. Place a layer of plastic wrap on top of the tin foil layer.
Sprinkle 1/3 of the curing ingredient mixture on top. Lay the salmon fillet (skin side down) on top of the cure mixture and spread another 1/3 of the mixture on the flesh side of the salmon.
Place the second salmon fillet and place it flesh side down on top of the first fillet.
Place another layer of plastic wrap, followed by another layer of foil, on top of both fillets and wrap up the ends so that the salmon and cure is tightly encased in the plastic and foil wrap.
Place the entire baking sheet in the refrigerator and top with another baking sheet. Place something heavy on top of the baking sheet so that the weight is distributed evenly along the salmon fillets.
Allow the fillets to cure in the refrigerator for 12-24 hours.
Mix together the sweet rub ingredients in a small bowl. Sprinkle the rub evenly over the flesh side of the salmon fillets and gently pat the rub into the fillets.
Shake off excess rub, lay fillets flat on baking sheet in a cool, dry place and allow to rest for 1 hour.
Set the salmon fillets skin-side down on the grill, keeping the dial set on "smoke." Smoke for 1-3 hours, or until a temperature inserted into the thickest part of the salmon registers 150F.
While the fish is smoking, be sure to monitor the temperature closely to ensure that it does not get above 160F. Enjoy!