Preheat your oven to 450°F (232°C).

In a dry skillet over medium heat, toast the coriander seeds and cardamom pods for about 3-4 minutes, or until fragrant. Let them cool, then crush them coarsely using a mortar and pestle or a spice grinder.

In a small bowl, combine the crushed coriander and cardamom with minced garlic, olive oil, salt, and black pepper. Rub this mixture all over the prime rib, ensuring it is evenly coated.

Place the seasoned prime rib on a rack in a roasting pan. Roast in the preheated oven for 20 minutes, then reduce the temperature to 325°F (163°C) and continue to cook for about 1.5 to 2 hours, or until the internal temperature reaches your desired doneness (135°F for medium-rare, 145°F for medium).

While the prime rib is cooking, melt 1/2 cup of the softened butter in a skillet over medium heat. Add the sliced leeks and cook, stirring occasionally, until they are soft and caramelized, about 15-20 minutes. Season with salt and set aside.

In a bowl, combine the remaining softened butter, caramelized leeks, fresh thyme, and lemon juice. Mix well until combined and set aside.

Once the prime rib is done cooking, remove it from the oven and tent it loosely with aluminum foil. Let it rest for at least 20-30 minutes to allow the juices to redistribute.

Slice the prime rib and serve it warm, topped with generous dollops of the caramelized leek butter.