Combine soy sauce, garlic, Worcestershire sauce, rosemary, black pepper, and olive oil in a bowl for the marinade.
Coat the prime rib with the marinade evenly in a large dish. Cover and refrigerate for at least 4 hours, or overnight.
Preheat the oven to 350°F (175°C).
Set the marinated prime rib on a roasting rack in a pan. Bake for 2-3 hours, aiming for 135-145°F internal temperature for medium-rare to medium doneness.
For preparing the sauce, simmer beef broth, Worcestershire sauce, red wine, salt, pepper, and Dijon mustard in a saucepan until it slightly thickens.
After removing from the oven, let the prime rib rest for 10-15 minutes before slicing.
Serve the prime rib with the Au Jus sauce on the side or drizzle over the meat. Enjoy your delicious roast!
Notes
For a more intense flavor, you can add additional herbs and spices to the marinade such as thyme, oregano, or paprika.
You can also experiment with different types of beef broth or red wine to create your own unique flavor profile.
If you prefer a thicker au jus sauce, you can stir in a tablespoon of flour or cornstarch to the mixture while it's simmering.