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

In a bowl, mix together the chopped green onions, minced garlic, olive oil, smoked paprika, kosher salt, black pepper, dried thyme, dried rosemary, and cayenne pepper, if using. Combine well to form a paste.

Pat the prime rib dry with paper towels. Rub the spice paste all over the roast, making sure to cover all sides evenly.

Preheat your oven to 450°F (232°C).

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

Reduce the oven temperature to 325°F (163°C) and continue roasting until the internal temperature reaches your desired doneness (125°F for rare, 135°F for medium-rare, and 145°F for medium). This usually takes about 15-20 minutes per pound.

Once the roast reaches the desired temperature, remove it from the oven and let it rest for at least 20-30 minutes before slicing. This allows the juices to redistribute.

In a medium bowl, combine the softened butter, chopped tarragon, chopped chives, lemon zest, and salt and pepper to taste. Mix until well incorporated. Transfer the mixture to a piece of plastic wrap, shape it into a log, and refrigerate until firm.

Slice the rested prime rib and serve with slices of tarragon chive butter on top. Enjoy your delicious charred green onion and garlic-crusted prime rib!