"This has come out perfect every time I have made it. You need to get your hands greasy on this one, but it's well worth it! It's succulent and savory - just what a prime rib should be! Pan juices from the roast can be added to the Au Jus at the last minute if need be."
Preheat oven to 500 degrees F (260 degrees C). Place a rack on a shallow roasting pan.
Coat entire roast with 1 cup softened butter. Set roast fat-side up on the rack.
Mix salt, tarragon, allspice, and black pepper together in a bowl. Rub salt mixture all over roast.
Bake roast in the preheated oven until outside is crisp and browned, about 50 minutes. Reduce oven temperature to 350 degrees F (175 degrees C). Continue baking roast until the internal temperature reaches 150 degrees F (65 degrees C), 35 to 40 minutes.
Remove roast from oven. Spoon pan juices into a small bowl; set aside. Cover roast with aluminum foil and let rest before slicing, 15 to 20 minutes.
Heat olive oil and 1 tablespoon butter in a large saucepan over medium heat. Add onions and cook until golden brown, about 5 minutes. Add mushrooms and cook until tender, about 10 minutes. Stir in water, beef broth base, and reserved pan juices. Simmer until flavors combine, 30 to 45 minutes. Serve au jus alongside roast.