Preheat your oven to 450°F (232°C). Let the prime rib sit at room temperature for about 1 hour before roasting to help it cook evenly.

In a dry skillet over medium heat, toast the allspice berries for about 2-3 minutes, or until fragrant. Remove from heat and let cool slightly. Crush the berries using a mortar and pestle or a spice grinder.

In the same skillet, add a drizzle of olive oil and the sliced leeks. Sauté over medium-high heat until they are charred and tender, about 5-7 minutes. Remove from heat and let cool.

Pat the prime rib dry with paper towels. Rub the roast generously with olive oil, then season with salt, pepper, and the toasted allspice. Press the charred leeks onto the surface of the roast to create an even crust.

Place the prime rib on a rack in a roasting pan. Roast in the preheated oven for 20 minutes. 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, 145°F for medium). This will take about 1.5 to 2 hours, depending on the size of the roast.

While the roast is cooking, melt 1 tablespoon of butter in a skillet over medium heat. Add the chopped shallots and cook until caramelized, about 10-12 minutes. Remove from heat and let cool. In a bowl, combine the softened butter, caramelized shallots, parsley, chives, salt, and pepper. Mix well until fully combined. Shape the compound butter into a log using parchment paper and refrigerate until firm.

Once the prime rib reaches the desired temperature, remove it from the oven and let it rest for at least 20 minutes before carving. This allows the juices to redistribute.

Slice the prime rib and serve with the caramelized shallot compound butter on the side. Garnish with fresh thyme sprigs.