Prepare the Smoked Garlic Confit: In a medium saucepan, combine the peeled garlic cloves and olive oil. Add smoked paprika, sea salt, and black pepper. Heat over low heat, allowing the garlic to slowly cook and infuse the oil. Simmer for about 45 minutes to 1 hour, or until the garlic is tender and golden. Remove from heat and let it cool. Transfer the garlic and oil to a jar and store in the refrigerator until ready to use.

Prepare the Cracked Cardamom-Crusted Prime Rib: Preheat your oven to 450°F (232°C). In a small bowl, combine the cracked cardamom, kosher salt, black pepper, garlic powder, rosemary, thyme, and olive oil to create a 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 prime rib on a roasting rack in a roasting pan. Roast in the preheated oven for 20 minutes to develop a crust. Lower the oven temperature to 325°F (163°C) and continue roasting until the internal temperature reaches 130°F (54°C) for medium-rare, about 1.5 to 2 hours. Use a meat thermometer for accuracy. Once done, remove the prime rib from the oven and let it rest for at least 20 minutes before slicing.

Prepare the Smoked Leek Compound Butter: In a mixing bowl, combine the softened butter, smoked leeks, chives, lemon zest, salt, and pepper. Mix until well combined. Place the compound butter on a sheet of parchment paper and roll it into a log shape. Twist the ends to seal and refrigerate until firm.

Serve: Slice the prime rib and serve it topped with a dollop of smoked leek compound butter. Drizzle with some of the smoked garlic confit oil for an extra layer of flavor.