Preheat smoker to 225˚F. Once it reaches this temperature, preheat with the lid closed for 10 to 15 minutes.
Remove turkey breast from brine (if using) or from packaging. If using straight from the packaging, rinse with cold water. Pat dry with paper towels.
Rub the outside with oil and season well with salt and pepper (or your favorite spice rub).
Place turkey breast on a roasting rack set inside a roasting pan. You can also set it on a wire rack set inside a rimmed baking sheet.
Place the pan directly on the grill grate or in your smoker. Insert probe, if using. Cook until the internal temperature reaches 100˚F to 110˚F. This took me about 3 hours for a 7 lb turkey breast.
Increase temperature to 350˚F. This will take another 1/2 hour to 1 hour, depending on turkey breast size. Continue to cook until a meat thermometer registers 162˚F to 164˚F when inserted into the thickest part of the breast.
Remove the roasting pan from the grill and let rest 15 to 20 minutes until the turkey is 165˚F before carving.