Remove the prime rib roast from the refrigerator and allow it to come to room temperature for about 1 hour before cooking.

In a small bowl, combine the smoked chipotle powder, crushed toasted coriander seeds, kosher salt, black pepper, and minced garlic. Mix well.

Rub the olive oil all over the prime rib roast. Then, generously apply the spice mixture, ensuring it coats the entire surface evenly.

Preheat your oven to 450°F (232°C).

Place the seasoned prime rib on a roasting rack in a roasting pan. 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 for about 1.5 to 2 hours, or until the internal temperature reaches your desired doneness (125°F for rare, 135°F for medium-rare, 145°F for medium).

In a mixing bowl, combine the softened unsalted butter, roasted garlic, chopped parsley, chopped thyme, and lemon zest. Mix until well combined and set aside.

Once the prime rib has reached the desired doneness, remove it from the oven and let it rest for at least 20 minutes. This allows the juices to redistribute throughout the meat.

Slice the prime rib and serve with dollops of the caramelized garlic compound butter on top.