Preheat your oven to 450°F (230°C).

In a small bowl, combine the toasted fennel seeds, smoked paprika, kosher salt, black pepper, minced garlic, olive oil, and Dijon mustard. Mix until a paste forms.

Rub the spice paste all over the prime rib roast, ensuring an even coating.

Place the seasoned prime rib on a roasting rack in a large roasting pan.

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 (about 120°F [49°C] for rare, 130°F [54°C] for medium rare, 140°F [60°C] for medium).

Remove the roast from the oven and tent with aluminum foil. Let it rest for at least 20-30 minutes before slicing.

In a medium bowl, combine the softened butter, chopped tarragon, chopped chives, lemon juice, salt, and pepper. Mix until well combined.

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

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