Remove the prime rib from the refrigerator about 1 hour before roasting. Pat thoroughly dry with paper towels.

Preheat the oven to 450°F. Place the roast bone-side down in a roasting pan fitted with a rack.

Combine the olive oil, garlic, rosemary, thyme, kosher salt, black pepper, onion powder and softened butter until evenly blended.

Rub the garlic herb mixture generously over the top and sides of the roast, pressing it onto the surface so it adheres.

Roast at 450°F for 20 minutes to begin developing a deeply browned exterior.

Reduce the oven temperature to 325°F and continue roasting until the center reaches your preferred doneness. Begin checking the internal temperature early rather than relying solely on cooking time.

Transfer the prime rib to a cutting board and loosely tent with foil. Rest for 30 minutes before carving. The internal temperature will continue to rise as the roast rests.

Carefully skim excess fat from the roasting pan, leaving the flavorful browned drippings. Place the pan over medium heat if stovetop-safe, or transfer the drippings to a saucepan. Add the beef broth, wine or additional broth, Worcestershire sauce and rosemary.

Scrape up the browned bits and simmer for 8–10 minutes, until flavorful and slightly reduced. Remove the rosemary and season with salt and pepper as needed.

Remove the bones if desired, slice the prime rib across the grain and serve warm with the au jus alongside.