Let the roast come to room temperature before cooking. This could take up to one hour. This step ensures the roast will cook evenly without hot spots on the top and raw meat in the middle.
Tie the roast with twine - see notes.
In a small bowl, combine softened butter, garlic, rosemary, thyme, kosher salt, and black pepper.
Pat the roast dry with paper towels to remove excess moisture.
Rub the butter mixture all over the roast and place the roast into a roasting pan.
Add chopped celery, onions, and carrots to the roasting pan and add 1 cup of beef broth to the roasting pan. Season the vegetables with salt and pepper and a drizzle of olive oil.
Preheat oven to 500º.
Cook the roast for 20 minutes uncovered at 500° to get a gorgeous crust and sear the meat. This also locks in the juices and is an essential step in cooking a prime rib.
After 20 minutes at 500°, decrease the oven temperature to 350º. Cook the roast to the desired doneness, about 12-15 minutes per pound for medium-rare.
Remove from the oven when an internal temperature of 130º is reached. You’ll know when the pop-up timer "pops" when the roast reaches 130°. Or use an instant-read thermometer placed into the thickest part of the roast, away from any bones or fat.
Let it rest 20-30 minutes in the roasting pan loosely tented with aluminum foil before slicing to serve.