Combine water, kosher salt, and dark brown sugar and stir until completely dissolved. Pour the brining solution into a baking or aluminum pan and add salmon into it.
Place a small plate or a food storage container filled with some dried beans to weigh down salmon into the brining solution. Make sure it’s not too heavy where it crushes the fish.
Place into the refrigerator for about 2 hours.
Prepare the smoker:
While salmon is brining, it's a good time to prepare smoker and get it to temperature.
Prepare your smoker and get the temperature to 225°. You will want to keep the temperature no higher than 225°. Place a drip pan with water under the grill grate if possible, or place it off to the side of the main grill grate. (This will depend on the type of smoker.)
Take salmon out of the brine and pat it dry with paper towels.
Gently rub your hand on the fillet to make sure there are no bones accidentally left behind. Use fish bone tweezers (or regular tweezers in a pinch) and take out any bones.
Season the filet with salt, peppers, and sugar.
Place salmon filet skin down on a sheet of aluminum foil.
Place the foil with salmon on the grate of the pre-heated smoker and smoke until internal temperature of salmon reaches 140°. (Make sure to start checking the temperature after 30 minutes on the smoker. Smaller/thinner fillets will be done faster.)
Take it off the smoker and let it rest for about 5 minutes before serving.