Prep the beef: Remove any excess fat or silver skin. Leave the fat cap on for now.
Season the beef: In a small bowl, mix together the all-purpose seasoning, chili powder, dried thyme, onion powder, mustard powder, and smoked paprika. Season the beef all over with the rub.
Prepare for grilling: Prepare your charcoal grill for direct heat grilling. Set it up so the coals are on one side, in case you need to move the beef to the other side. *You can cook with the grill open but be very careful with the flame as the fat from the beef will throw flames.
While the grill is heating up, make the tiger sauce: In a small bowl, mix together the sour cream, mayonnaise, and horseradish. Season with black pepper to taste. Cover and transfer the sauce to the refrigerator until ready to serve.
Sear the beef: Add the beef to the grill and allow it to cook on the first side about 5-7 minutes, or until a nice crust develops. Then flip to the second side for an additional 5-7 minutes. Carefully roll it every 5-6 minutes to develop a nice sear on all sides. Once it’s seared on all sides and the internal temperature reaches about 70℉ (about 30 minutes), remove from the grill and cut off the fat cap. *Cooking times will vary based on the size of your beef roast and the temperature of your grill.
Finish cooking the pit beef: Add the beef back to the grill. Do not re-season after cutting off the fat cap. Cook the beef until it reaches an internal temperature of 110-112°F on an instant-read thermometer inserted into the beef. *Our total cooking time was about 1 hour, but times will vary. Remove from the grill and let it rest for 20 minutes.
Slice the beef: Use a meat slicer or a sharp knife to thinly slice the beef into deli-style slices against the grain.
Make the sandwiches: Toast the buns. Spread the tiger sauce on the top buns. Place a generous serving of sliced beef on top of the bottom buns, then layer with sliced onions and the top of the buns. Serve immediately.