After the Brine, remove the turkey from the brine solution and rinse thoroughly. Pat dry and then coat liberally with coarse black pepper. The salt flavor is already inside of the meat due to the brine.
Smoke the turkey breast in a smoker around 250-275°F. After an hour and a half, remove the turkey from the smoker, and wrap in foil covered with butter. Place back on the smoker and continue cooking it until the breast meat is 160°F. Remove from the smoker and rest for 15 minutes.