Preheat your oven to 450°F (230°C).

In a small bowl, combine the olive oil, smoked paprika, kosher salt, and cracked black pepper. Rub this mixture all over the prime rib roast, ensuring it is well-coated.

In a roasting pan, spread the sliced leeks evenly on the bottom. Place the coated prime rib on top of the leeks.

Insert the roast into the preheated oven and roast at 450°F (230°C) for 20 minutes. This initial high heat will create a nice crust on the meat.

After 20 minutes, reduce the oven temperature to 325°F (160°C) and continue roasting for approximately 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).

While the roast is cooking, melt the room-temperature butter in a small saucepan over medium heat. Add the minced shallots and cook, stirring frequently, until the shallots are golden brown and fragrant, about 5-7 minutes. Remove from heat and stir in the thyme, rosemary, Dijon mustard, minced garlic, and lemon zest. Let it cool slightly.

Once the prime rib is done roasting, remove it from the oven and let it rest for 20-30 minutes before slicing. This allows the juices to redistribute throughout the meat.

Slice the prime rib and serve it on a platter, drizzling it with the browned shallot confit butter. Garnish with fresh herbs if desired.