Step 1: Set up your smoker following the manufacturer’s instructions and preheat to 225° to 250°F. Add the wood as specified by the manufacturer.
Step 2: Place the tenderloin on a rimmed baking sheet and season very generously on all sides with salt and pepper. Drizzle the tenderloin on all sides with olive oil, rubbing it into the meat.
Step 3: Place the tenderloin in the smoker and insert the probe of your remote thermometer (if using) through the thick end of the tenderloin into the center. (Alternatively, check for doneness toward the end of cooking, using an instant-read thermometer.) Smoke the tenderloin until the internal temperature is about 110°F, 45 to 60 minutes. Transfer it to a platter and let it rest for 10 minutes.
Step 4: Meanwhile, set up your grill for direct grilling and preheat to high. Brush and oil the grill grate. If you happen to be smoking on a charcoal grill, rake the coals into a mound, after the smoking is completed, adding fresh coals as needed, to build a hot fire.
Step 5: Transfer the tenderloin to the grill, with the thermometer probe still attached. Direct grill, rotating it like a log, until all sides are crusty, dark, and sizzling and the internal temperature in the thickest part of the tenderloin reaches 120° to 125°F (for rare beef) or 130° to 135°F (for medium-rare), 6 to 10 minutes. Brush the tenderloin with additional olive oil as it grills, and if you like, give it a quarter turn on each side halfway through grilling to lay on a crosshatch of grill marks.
Step 6: Place the tenderloin on a cutting board and remove the strings. Cut the meat crosswise into ¼- to ½-inch-thick slices. It just may be the best beef tenderloin you’ll ever taste.
Note: Upright barrel smokers like the Pit Barrel Cooker work great for smoking beef tenderloin. Hang the tenderloin head end up from the meat hook. You can smoke and cook it simultaneously—there’s no need for separate smoking and grilling. (The PBC runs at just shy of 300°F.) Cooking time will be 45 minutes to 1 hour. Use a kamado-style cooker, like the Komodo Kamado, the same way. On a pellet grill, like the Memphis Wood Fire Grill, smoke the tenderloin low and slow, then remove the burn chamber cover and finish the tenderloin by direct grilling.