In a medium bowl, make the brine by whisking together the water, kosher salt, and brown sugar. Place your fish in the bowl with the brine. Cover and refrigerate for 8 to 12 hours.
Take your fish out of the brine, rinse it under cool running water, and pat it dry with paper towels. Set the fish fillets on a cooling rack, skin side down, on top of a rimmed baking sheet. Place the fish in the refrigerator, uncovered, for at least 4 hours (or up to overnight). You want the fish to dry out in order to form a sticky layer on the outside, called a pellicle. This will help the smoke cling to the fish.
Preheat your smoker to 150 degrees F. Don't try to rush the process and set the temperature any higher! If you've ever smoked or baked fish at a higher temperature, you may have had it "bleed" an unpleasant looking white, creamy substance, that congeals on the top of the fillet. This is NOT good. The pellicle that just formed from drying the fish in the refrigerator, as well as smoking at a low temperature, will prevent this from happening. The low and slow smoking process allows the fish to absorb the smoky flavor while retaining moisture and tenderness.
Add your choice of wood chips to the smoker. Popular wood chips include alder, hickory, apple, cherry, and oak. Most folks don't appreciate the strong flavor of mesquite, but my wife and I are huge fans, so I used mesquite wood chips when making this recipe. Don't be afraid to experiment with whatever wood chips you prefer.
Remove the fish from the refrigerator and brush the fish with some olive oil so it won't stick to the smoker rack. Place the fish, skin side down on the smoker rack for one hour, then finish at 180 degrees F for the last hour or two.
After an hour in the smoker, baste the fish with honey or maple syrup. Baste the fish about every 45 minutes until the fish is done.
Once your fish is smoked for a total of about 3 to 4 hours and reaches an internal temperature of 140 degrees F, let it rest on a cooling rack at room temperature for 30 minutes. Enjoy warm or chilled.