Mix the water, salt, and brown sugar in a large bowl, and stir well until the salt and sugar dissolve. Add the soy sauce, garlic, ginger, green onions, black pepper, and pepper flakes.
Submerge the tuna steaks in the brine, or place them in a large ziplock bag and pour the brine over them until submerged. Add more brine if needed.
Cover the bowl with plastic wrap or close the seal on the ziplock bag and brine in the refrigerator for 45 minutes to an hour. If the steak is especially thick, you could go up to 2 hours. Brining tuna for too long will make it extremely salty and mushy.
Pull the tuna steaks from the brine, and gently pat them dry with paper towels. If you have time, let them air-dry in the refrigerator for 1-2 hours to form film that will absorb the smoke better and keep the fish moist.
Preheat the smoker or pellet grill to 175-225°F (80-107°C). The lower the temperature, the longer it will take, but the moister the meat will be.
Place the tuna directly on the grates, and optionally brush them with olive oil. Smoke them until they reach the desired internal temperature.
It usually takes 20-30 minutes to reach 115-120°F (45-50℃) for rare (sashimi). If smoking at 125-130°F (52-55℃), it may take 45-60 minutes. And for well-done (if you're using it for dips later), 1-1½ hours or an internal temperature of 140-145°F (60-62℃) works best. The fish flakes easily.
Take the tuna steaks out of the smoker and enjoy them immediately with your chosen sides. There's no need to let them rest.