Allow the Prime Rib to come to room temperature by sitting on the counter for roughly 30 minutes before cooking.
With softened butter, mix in chopped rosemary, garlic, salt, and pepper. Coat the prime rib with this entirely.
Pour the beef broth into the bowl of your pressure cooker, and the place in your prime rib on a rack.
Set the pressure cooker for 5 minutes. After the timer has finished, allow the pressure cooker to come to a full natural release, around 30 minutes.
Remove the prime rib from the pressure cooker and use a meat thermometer to check the temperature. I prefer mine to be around 10 degrees below desired as we will further cooking it when we add the sear. If it is not at your desired temperature, continue to let it warm in the pressure cooker- but do not add any more time.
In a cast iron or heavy bottom pan, heat the olive oil until nearly smoking. Brown your prime rib on all sides. Rest your prime rib for 10 minutes before carving- and then enjoy!