Preheat pellet grill or smoker to 200-225 degrees F with your choice of wood pellets.
Pat the tenderloin dry with paper towels, then season all sides with a 50/50 blend of Texas Rub and Shake That All Purpose seasoning (or all-purpose seasoning of your choice). *Alternatively, you can place the tenderloin on a wire cooling rack set on top of a sheet tray and refrigerate overnight to dry it before seasoning.
Make the horseradish rub. Combine softened butter, horseradish, Worcestershire sauce, dijon mustard, mayo, garlic, and rosemary in a medium bowl. Mix together well.
Spread the horseradish rub in an even layer all over the tenderloin. *The recipe for the horseradish garlic butter rub is just the right amount for a 5-6 pound beef tenderloin. If your roast is smaller than that, you may want to adjust the recipe down.
Place the tenderloin directly on the grill grates and close the lid. Smoke the beef tenderloin until it reaches an internal temperature of about 100-105 degrees F. Then, remove the tenderloin from the grill. *This may take about 1½-2 hours, but total cooking time will depend on the size of your tenderloin and the temp of your grill.
While the tenderloin is smoking, melt ½ stick butter in a small bowl or saucepan with 2 cloves of minced garlic and set aside. This will be the basting sauce for later.
With the tenderloin off of the grill, increase the pellet grill temp to 450 degrees F. When the grill reaches that temp, place the smoked beef tenderloin back on the grill to sear until the internal temp reaches about 120-125 for medium rare, flipping every 2-3 minutes. As beef is searing, baste every 2-3 minutes with the melted butter and garlic. *If your pellet grill has an open-flame option, then adjust the baffle plate/diffuser to sear the beef over the open flame.
Remove the smoked beef tenderloin from the grill and let rest for about 15-20 minutes. The internal temp of the beef will continue to rise during this time, and may rise as much as 5-6 degrees, so be sure to account for that when temping the meat. After the resting period, slice into medallions about ½" – ¾ " thick, depending on preference. Serve warm with horseradish sauce or your favorite steak toppings.