Remove the prime rib from the refrigerator and let it sit at room temperature for about 1 hour before cooking to ensure even cooking.

In a small bowl, combine smoked sea salt, cracked black peppercorns, garlic powder, onion powder, dried thyme, and cayenne pepper (if using).

Rub the olive oil all over the prime rib, then generously coat the roast with the seasoning mixture, pressing it into the meat to adhere.

Preheat your oven to 450°F (230°C).

Place the seasoned prime rib on a roasting rack in a roasting pan, bone side down. Roast in the preheated oven for 20 minutes to develop a crust.

Lower the temperature to 325°F (160°C) and continue to roast for approximately 15-20 minutes per pound for medium-rare, or until the internal temperature reaches 130°F (54°C). Use a meat thermometer for accuracy.

Once done, remove the prime rib from the oven and cover it loosely with aluminum foil. Let it rest for at least 20-30 minutes to allow the juices to redistribute.

In a bowl, combine the softened unsalted butter, chopped tarragon, chopped chives, and lemon juice. Mix well until all ingredients are incorporated. Season with salt and pepper to taste.

Transfer the butter to a piece of parchment paper or plastic wrap, shape it into a log, and refrigerate until firm.

Slice the rested prime rib and serve with generous dollops of tarragon chive butter on top.