Preheat your oven to 450°F (230°C).

In a small bowl, combine the cracked cardamom, smoked paprika, toasted coriander, kosher salt, and black pepper. Mix well to form a spice rub.

Pat the prime rib roast dry with paper towels. Rub the olive oil all over the roast. Then, generously apply the spice rub, ensuring that the entire surface is coated.

In a roasting pan, arrange the sliced leeks and halved shallots. Drizzle them with olive oil and season with salt and pepper. Toss to coat evenly.

Place the prime rib on top of the leeks and shallots in the roasting pan. Roast in the preheated oven for 20 minutes to develop a crust.

After 20 minutes, reduce the oven temperature to 325°F (165°C) and continue to roast the prime rib for about 1.5 to 2 hours, or until the internal temperature reaches your desired doneness (125°F for medium-rare, 135°F for medium).

While the prime rib is roasting, prepare the roasted shallot butter. In a medium bowl, combine the softened butter, minced garlic, fresh thyme leaves, lemon zest, and a pinch of salt and pepper. Mix until well combined. Set aside.

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

Slice the prime rib and serve it with the roasted leeks and shallots. Top each serving with a generous dollop of the roasted shallot butter.