Preheat your oven to 450°F (230°C). Pat the prime rib roast dry with paper towels. Rub the olive oil all over the roast, then season generously with salt and freshly ground black pepper.

In a small bowl, combine the chopped rosemary, minced garlic, Dijon mustard, and whole mustard seeds. Mix well to form a paste. Evenly spread the herb paste over the top and sides of the prime rib, pressing it into the meat to adhere.

Heat a grill pan or cast-iron skillet over medium-high heat. Add the halved leeks cut-side down and char until they are golden and slightly softened, about 3-4 minutes. Remove from heat.

Place the charred leeks around the prime rib in a roasting pan. Insert a meat thermometer into the thickest part of the meat. Roast in the preheated oven for 20 minutes to develop a nice crust.

Lower the oven temperature to 325°F (165°C) and continue roasting until the internal temperature reaches your desired doneness (125°F for rare, 135°F for medium-rare, 145°F for medium), about 1.5 to 2 hours, depending on the size of the roast.

In a mixing bowl, combine the softened butter with the chopped parsley, thyme, chives, smoked paprika, and lemon juice. Mix until well combined. Transfer to a sheet 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 at least 20 minutes before carving. Slice the prime rib and serve with the charred leeks and a generous dollop of smoked herb butter on top.