Preheat the oven to 250°F (120°C). In a small baking dish, combine the peeled garlic cloves, olive oil, thyme, rosemary, and sea salt. Cover with aluminum foil and roast for about 2 hours, until the garlic is soft and golden. Remove from oven, let cool, and store in a jar with the oil.

Preheat the oven to 450°F (230°C). In a bowl, mix the cracked pink peppercorns, Dijon mustard, smoked paprika, kosher salt, black pepper, mashed roasted garlic, and chopped rosemary to create a paste. Rub the paste evenly over the prime rib roast.

Place the roast bone-side down on a rack in a roasting pan. Roast for 20 minutes, then reduce the temperature to 325°F (160°C) and 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. Remove from oven and let rest for at least 20 minutes before slicing.

In a mixing bowl, combine the softened butter, chopped tarragon, chopped chives, and lemon juice. Season with salt and pepper to taste and mix until well combined. Shape the butter into a log using parchment paper, twist the ends to seal, and refrigerate until firm.

Slice the rested prime rib and serve with a generous dollop of tarragon chive butter on top and a side of roasted garlic confit.