Combine the water, salt, and 1 tbsp of the bbq rub in a saucepan and bring to a boil.
Let the brine boil for a minute and then remove from the heat and let it come down to room temp.
Add a cup of ice to a sealable container and then add the turkey breast and the brine. Make sure the breast is completely submerged. Place the container in the fridge.
Brine the turkey breast for 6 hours. When you're ready to cook remove the breast from the brine and pat dry. Season the exterior of the breast with the remaining bbq rub.
Smoke the breast at 275 degrees until the internal temperature hits 145 degrees.
Adjust the temperature of the smoker up to 375 and continue cooking the turkey until the internal temperature hits 160.
Let the breast rest on a cutting board for about 15 minutes before slicing.