Take the prime rib roast out of the refrigerator and allow it to come to room temperature (about 1 hour). Preheat your smoker or grill to 225°F (107°C).

In a small bowl, combine smoked guajillo chili powder, ground toasted coriander, kosher salt, and black pepper. Mix well.

Rub the roast with olive oil, ensuring it is evenly covered. Sprinkle the spice rub all over the roast, pressing it into the meat.

In a medium bowl, combine softened butter, minced garlic, fresh thyme, fresh rosemary, chopped parsley, and lemon juice. Mix until well combined. Transfer the compound butter onto a sheet of plastic wrap, shape it into a log, and refrigerate until firm.

Slice the top off the head of garlic to expose the cloves. Drizzle with olive oil, wrap in foil, and place it in the smoker.

Place the seasoned prime rib on the smoker grates, away from direct heat. Close the lid and smoke for approximately 4-6 hours, or until the internal temperature reaches your desired doneness (135°F for medium-rare). During the last hour of smoking, add the wrapped garlic to the smoker.

Once the garlic is soft and caramelized (about 45 minutes), remove it from the smoker, let it cool slightly, then squeeze the cloves out of their skins into the compound butter mixture. Mix well to combine.

Once the prime rib reaches your desired temperature, remove it from the smoker and tent it loosely with foil. Allow it to rest for at least 20-30 minutes before slicing.

Slice the prime rib roast and serve warm with the caramelized garlic compound butter on the side.