Preheat your oven to 450°F (232°C).

In a large skillet over medium heat, add 2 tablespoons of olive oil. Once hot, add the sliced shallots and cook until caramelized, about 15-20 minutes. Stir occasionally to prevent burning. Remove from heat and set aside.

In a small bowl, mix together the smoked paprika, salt, and black pepper.

Rub the prime rib roast all over with the remaining 2 tablespoons of olive oil. Then, coat the roast evenly with the smoked paprika mixture, pressing it into the meat.

Place the roast bone-side down in a roasting pan. Scatter the caramelized shallots over and around the roast.

Roast the prime rib in the preheated oven for 20 minutes. Then, 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 prime rib is roasting, prepare the browned garlic butter. In a small saucepan over medium heat, melt the butter. Add the minced garlic and cook until golden brown, about 2-3 minutes. Remove from heat.

Once the prime rib is done, remove it from the oven and let it rest for at least 20 minutes before slicing. This allows the juices to redistribute.

To serve, slice the prime rib and drizzle with the browned garlic butter. Garnish with fresh herbs.