Preheat your oven to 450°F (232°C).

In a small bowl, mix together the smoked guajillo chili powder, ground toasted coriander, kosher salt, and black pepper.

Rub the prime rib roast all over with olive oil, ensuring even coverage.

Generously coat the roast with the spice mixture, pressing it into the meat for better adhesion.

Place the seasoned roast on a rack in a roasting pan, bone side down.

Roast in the preheated oven for 20 minutes to develop a crust.

After 20 minutes, reduce the oven temperature to 325°F (163°C) and continue roasting until the internal temperature reaches your desired doneness (about 130°F for medium-rare, approximately 1.5 to 2 hours).

While the roast is cooking, prepare the caramelized shallot compound butter. In a skillet over medium heat, melt 2 tablespoons of butter and add the sliced shallots.

Cook the shallots, stirring frequently, until they are caramelized and golden brown, about 15-20 minutes. Remove from heat and let cool slightly.

In a mixing bowl, combine the softened butter, caramelized shallots, thyme, parsley, and minced garlic. Mix until well combined.

Once the roast reaches the desired temperature, remove it from the oven and let it rest for at least 20 minutes before slicing. This allows the juices to redistribute.

Serve the sliced prime rib roast with a generous dollop of the caramelized shallot compound butter on top.