Preheat smoker to 275°F and add a few chunks of apple wood or other wood of your choice.
Combine salt, pepper, paprika, and garlic powder in a small bowl and stir to combine. Coat the turkey breast with the olive oil then sprinkle on the seasoning mixture.
Add the turkey to the smoker and cook until it reaches an internal temperature of around 157°F. Brush the skin with the melted butter then continue to smoke until it reaches 160°F.
Remove the turkey and tent with foil. Let rest for 20 minutes before carving.