Preheat an outdoor pellet smoker to 225 degrees Fahrenheit (107 degrees Celsius).
Rub the pork tenderloin with 1 tablespoon olive oil thoroughly to coat.
In a small bowl, stir together 1 1/2 teaspoons salt, 1 teaspoon black pepper, 1 teaspoon smoked paprika, 1/2 teaspoon onion powder, and 1/2 teaspoon garlic powder. Season the tenderloins, ensuring all sides are well coated.
Place the pork tenderloins directly on the smoker rack, leaving a little space between each to allow air to circulate. Close the lid. Smoke until the internal temperature reaches 135 degrees Fahrenheit (57 degrees Celsius), about 45 minutes. Cooking time may vary depending on the thickness of the tenderloin. Use a meat thermometer or internal probe for accuracy.
Remove the pork from the smoker and place it on a large baking sheet. Loosely wrap in aluminum foil.
Increase smoker temperature to 400 degrees Fahrenheit (204 degrees Celsius). Melt 4 tablespoons salted butter. Return the tenderloins to the smoker and baste with the melted butter.
Continue cooking until the internal temperature reaches 145 degrees Fahrenheit (63 degrees Celsius), about 10 to 15 minutes.
Remove the tenderloin from the smoker. Rest uncovered for 5 to 10 minutes before slicing.
Notes
For a sweet and fruity smoke, go with fruitwood pellets like apple or cherry. If you’re after that classic Southern barbecue flavor, hickory pellets are the way to go.