Prep the turkey breast. Pat the turkey dry with paper towels. Place it on a wire cooling rack set on top of a sheet tray. Refrigerate uncovered for at least 2 hours, or overnight for best results.
Season. Rub the breast all over with olive oil. Then mix all of the dry seasonings in a bowl and coat the turkey evenly. *See notes on seasoning.
Set up the grill for indirect cooking. Charcoal: Place lit coals on one side only. Gas: Turn on one burner (medium-low) and leave the other off. Preheat the grill or smoker to about 250-275℉.
Smoke the turkey breast. Place the turkey on the cool side of the grill (indirect heat). Close the lid and cook until the internal temperature reaches 160°F in the thickest part (expect 40-50 minutes per pound at this temperature range, but always cook to the correct internal temperature NOT to a specific time).
Check for doneness. Use a probe thermometer to make sure the internal temperature has reached 160°F in the thickest part of the breast.
Butter wrap and rest. Place 3 cubes of butter on a large sheet of heavy-duty foil. Carefully remove the hot turkey from the grill and set it on top of the butter, then place the remaining 3 cubes on top of the turkey breast. Wrap the foil tightly around the turkey, creating a sealed packet. The residual heat should melt the butter immediately. Rest the wrapped turkey for 20–30 minutes during which the internal temperature will rise to 165°F and the juices will settle.
Slice and serve. Carefully unwrap the turkey, reserving the melted butter. Slice the turkey against the grain and drizzle the reserved melted butter from the foil over the slices before serving.