Make the brine: Combine brown sugar and salt in a small bowl.
Brine the Salmon: Place salmon skin-side down on a wire rack over a rimmed baking sheet. Evenly sprinkle the brine mixture over the top of the salmon filet.
Refrigerate uncovered for at least 1 hour (and up to 8 hours).
Preheat Your Smoker to 225°F: Set it up for indirect heat with a water bath drip pan and wood chips/pellets.
Remove salmon from the refrigerator and pat dry with paper towels (there is no need to rinse it).
Smoke the Salmon: Place salmon skin-side down on a sheet of foil and transfer it to the smoker.
Check for doneness after 30 minutes using a probe thermometer. It is done cooking when the internal temperature reaches 140°F in the thickest part.
Rest: Remove from the smoker and rest for 5 minutes before serving, or cover tightly and chill in the refrigerator for up to 1 week.