Preheat your oven to 450°F (230°C).

In a large bowl, combine the smoked paprika, kosher salt, black pepper, minced garlic, olive oil, thyme, rosemary, and Dijon mustard. Mix well to create a paste.

Pat the prime rib roast dry with paper towels. Rub the spice paste over the entire surface of the roast, ensuring an even coating.

Place the quartered shallots in the bottom of a roasting pan. Place the seasoned prime rib on top of the shallots, bone side down.

Pour the beef broth into the bottom of the roasting pan to keep the roast moist during cooking.

Roast the prime rib in the preheated oven for 15 minutes, then reduce the temperature to 325°F (160°C). Continue roasting until the internal temperature reaches 130°F (54°C) for medium-rare, about 1.5 to 2 hours, depending on the size of the roast.

While the roast is cooking, prepare the smoked leek compound butter. In a bowl, combine the softened butter, chopped leeks, parsley, lemon zest, salt, and pepper. Mix until well combined. Transfer the mixture to a piece of plastic wrap, shape into a log, and refrigerate until firm.

Once the prime rib has reached the desired temperature, remove it from the oven and let it rest for 20-30 minutes before slicing. This allows the juices to redistribute.

To serve, slice the prime rib and top each slice with a dollop of the smoked leek compound butter. Serve with the roasted shallots from the pan.