If brining, place turkey breast in brine solution and refrigerate for 12-24 hours.
After brining, rinse turkey breast with cold water and pat dry with paper towels. Apply olive oil to make a binder, and season with poultry or bbq seasoning.
Smoke turkey breast at 225°F, until the internal temperature reaches 150°F. (About 1.5-2 hours) Wrap turkey breast in aluminum foil with pats of butter, and place back onto the smoker until it reaches 165°F. (30 minutes to an hour).
Rest turkey breast for 15 minutes with foil vented. Slice and serve.