Preheat your oven to 450°F (232°C).

In a small bowl, combine the smoked pasilla chili powder, crushed toasted fennel seeds, kosher salt, cracked black pepper, and minced garlic. Add olive oil to form a paste.

Rub the spice paste all over the prime rib roast, making sure to cover every surface. Allow the roast to sit at room temperature for about 30 minutes to an hour.

Place the seasoned roast on a rack in a roasting pan. Insert a meat thermometer into the thickest part of the roast. Roast in the preheated oven for 20 minutes to develop a crust.

After 20 minutes, reduce the oven temperature to 325°F (163°C) and continue roasting until the internal temperature reaches your desired doneness (130°F for medium-rare, approximately 1.5 to 2 hours total cooking time).

Once cooked to your liking, remove the roast from the oven and let it rest for at least 20-30 minutes before carving. This allows the juices to redistribute.

In a skillet over medium heat, melt 1 tablespoon of butter. Add the finely chopped shallots and cook until they are golden brown and caramelized, about 10-15 minutes. Stir in the chopped thyme and balsamic vinegar, and season with salt and pepper. Remove from heat and allow to cool slightly.

In a mixing bowl, combine the remaining softened unsalted butter with the caramelized shallot mixture. Mix well until fully incorporated.

Slice the prime rib roast and serve with a generous dollop of the caramelized shallot compound butter on top.