Pat the beef tenderloin dry with paper towels. Rub it all over with olive oil and Worcestershire sauce to help the spices stick.
Apply the Cajun Rub
In a small bowl, mix all the Cajun rub ingredients together. Generously coat the entire tenderloin, pressing the seasoning into the meat to form a crust. Let it sit at room temperature for 20 minutes.
Preheat the Grill
Set up your grill for two-zone cooking—one side with high heat (direct grilling) and the other cooler (indirect heat). Heat the grill to 400°F.
Sear the Tenderloin
Place the beef directly over high heat and sear for 2-3 minutes per side, turning to get a good crust.
Cook Over Indirect Heat
Move the tenderloin to the cooler side of the grill. Close the lid and cook until the internal temperature reaches 125°F for medium-rare (about 20-25 minutes). Baste with melted butter occasionally for extra flavor.
Rest & Serve
Remove from the grill and tent loosely with foil. Let it rest for 10 minutes before slicing. This allows the juices to redistribute, keeping the meat juicy.