Trim beef tenderloin. Cut off the tail, remove the butt end for a uniform center cut whole tenderloin, save the scraps for other dishes. Remove the silver skin and excess fat.
In a small bowl, combine dry rub ingredients. Coat the trimmed beef tenderloin with the olive oil, and liberally apply the dry rub to the tenderloin. Cover tenderloin in plastic wrap and store in the refrigerator for 2-3 hours prior to cooking.
Remove the tenderloin from the refrigerator and remove from plastic wrap. Prepare your smoker using apple or other fruit wood at 250 degrees Fahrenheit.
Place the tenderloin on the smoker until the internal temperature reaches 130 degrees. This should take approximately 45 minutes to an hour. Once the temperature of the meat reaches 130 degrees remove tenderloin.
Prepare grill for high heat or direct grilling. Grill tenderloin 3 minutes per side and remove when the internal temperature of the tenderloin is 140 degrees F, about 8 – 12 minutes total. You will find the tenderloin has roughly three sides as it smokes and makes it easy to rotate.
Remove from heat and let rest prior to slicing, this is when carry over cooking will take the internal temperature to 145 degrees F. Prepare compound butter by combining all ingredients in a small bowl. Slice the tenderloin into 2-ounce medallions, and serve two to a dish. Using a spatula add about ½ tablespoon of compound butter to the warm steak where it will melt.