Preheat your oven to 450°F (232°C).

Pat the prime rib roast dry with paper towels and season generously with kosher salt and freshly cracked black pepper. Let it sit at room temperature for about 1 hour.

In a large skillet, heat the olive oil over medium heat. Add the sliced leeks and cook, stirring occasionally, until they are caramelized and golden brown, about 15-20 minutes. Remove from heat and set aside.

In a separate bowl, mix together the smoked shallots, thyme, rosemary, and minced garlic with the softened butter until well combined. Set aside.

Place the seasoned prime rib on a rack in a roasting pan. Spread the caramelized leeks evenly over the top of the roast.

Roast the prime rib in the preheated oven for 15 minutes, then reduce the temperature to 325°F (163°C) and continue cooking until the internal temperature reaches your desired doneness (about 130°F (54°C) for medium-rare), approximately 1.5 to 2 hours, depending on the size of the roast.

During the last 15 minutes of roasting, spread the smoked shallot butter mixture over the top of the roast.

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

Slice the prime rib and serve it warm, garnished with any remaining caramelized leeks and fresh herbs if desired.