Remove prime rib from the refrigerator about an hour before baking. Place unwrapped prime rib in a roasting pan fitted with a roasting rack; allow the prime rib to come to room temperature.
Preheat oven to 450 degrees for 30 minutes while the prime rib comes to room temperature.
In a small bowl, combine the softened butter, garlic, herbs, salt and pepper. Rub the herb butter over the entire prime rib; place on the rack fat side up.
Roast the prime rib at 450 degrees for 20 minutes; reduce the oven temperature to 350 degrees. Continue to cook until a meat thermometer reads 120-125 degrees (Estimate about 15 minutes of cooking time per pound of prime rib) about 1 hour and 15 minutes to 1 hour and 45 minutes. The internal temperature will continue to rise while the meat rests, resulting in a perfectly cooked Medium Rare 130-135 degrees.
Once desired temperature is reached, remove prime rib from the oven and tent with foil; rest for 20 minutes.
GRAVY: Meanwhile, pour the pan drippings into a saucepan over medium heat. Add the flour, whisking until there are no lumps, then add the beef stock, stirring until the sauce comes to a boil. Remove from heat, season with salt and pepper to taste; strain the sauce into a gravy dish.
Remove the prime rib from the pan to a carving board. Carve the prime rib into 3/4-inch slices. Serve with mashed potatoes, gravy, and green beans if desired.
Cook’s Notes: When buying prime rib estimate a 1-lb. per person.
For a perfectly cooked prime rib, buy a digital meat thermometer, it provides an accurate temperature and prevents overcooking. Rare: 120-125 degrees, Medium Rare: 130-135 degrees, Medium Well: 140-145 degrees