Preheat your oven to 450°F (232°C).

In a skillet over medium heat, add olive oil and the sliced shallots. Cook, stirring occasionally, until the shallots are caramelized and golden brown, about 15-20 minutes. Remove from heat and set aside to cool.

In a small bowl, combine the crushed pink peppercorns, sea salt, black pepper, garlic powder, and onion powder. Mix well to create the spice rub.

Pat the prime rib roast dry with paper towels. Rub the spice mixture all over the roast, ensuring it is evenly coated.

Place the roast on a rack in a roasting pan, bone-side down. Roast in the preheated oven for 20 minutes to develop a crust.

Meanwhile, prepare the smoked leek butter. In another skillet, melt 2 tablespoons of unsalted butter over medium heat. Add the leeks and sauté until tender, about 5-7 minutes. Stir in the smoked paprika and cook for an additional minute.

Once the leeks are cooked, remove from heat and mix in the remaining 2 tablespoons of softened butter until fully combined. Season with salt and pepper to taste. Set aside.

After the initial roasting time, reduce the temperature to 325°F (163°C) and continue to roast the prime rib for about 1.5 to 2 hours, or until the internal temperature reaches your desired doneness (125°F/52°C for medium-rare).

Remove the prime rib from the oven and let it rest for at least 20 minutes before slicing. This allows the juices to redistribute.

Serve the prime rib slices topped with caramelized shallots and a generous dollop of smoked leek butter. Garnish with fresh herbs if desired.