Preheat the oven to 500°F.
Using a hand mixer, cream the room-temperature butter for 1 minute until light and fluffy. Then, apply it to every surface of the roast using your hands or a spatula.
Sprinkle salt and pepper generously over the buttered surface of the roast.
Place the seasoned prime rib, fat side up, in the Dutch oven, with the butcher's twine still on. Place uncovered in the preheated oven for 15 minutes.
Reduce the oven temperature to 325°F and cook according to your desired doneness. For medium rare, cook the prime rib in the Dutch oven for 10 to 12 minutes or use an instant-read thermometer to check the meat's internal temperature.
Turn the oven off, but do not open the door. Leave the prime rib undisturbed for 1 to 2 hours.
After the full resting period, transfer the prime rib to a cutting board, remove the butcher's twine, slice, and serve. Enjoy!