Garlic and Rosemary Prime Rib with Red Wine Mushroom Sauce

Position the oven rack in the middle of the oven to achieve optimal heat distribution and preheat it to 250 degrees Fahrenheit (or 120 degrees Celsius). \nHeat a 12-inch oven-safe skillet over high heat, allowing it to reach its maximum temperature. Anoint the roast with oil, sprinkling salt and pepper liberally on all sides. Turn on your kitchen's ventilation system to prevent cooking fumes from accumulating and add the roast to the scorching skillet. Sear the roast on all sides for approximately 10 minutes, resulting in a perfectly browned crust. Remove the roast from the skillet and place it on a plate to cool slightly.\nOnce the roast has cooled enough to handle, take a moment to prepare it for its next stage of cooking. Mince garlic and rosemary, then spread them evenly across the roast's surface.\nCarefully pour off all but 2 tablespoons of the rich beef drippings from the skillet, leaving a small amount to add moisture and flavor. Add sliced mushrooms to the hot skillet and sauté them until they are beautifully browned, taking around 8 minutes to achieve this. Mix a combination of broth, wine, and mustard in a small bowl, then add it to the skillet with the mushrooms. Simmer the mixture for 3 minutes, allowing the flavors to meld together and slightly reduce.\nTransfer the mushroom sauce to a separate bowl, setting it aside for later use. Place a wire rack over the skillet and carefully position the roast on top of it, ensuring that it is secure. Slow-cook the roast in the oven until it reaches an internal temperature of 135 degrees Fahrenheit (or 57 degrees Celsius) for medium-rare, or 140 degrees Fahrenheit (or 60 degrees Celsius) for a medium-cooked roast. This process should take around 2 1/2 to 3 hours.\nTransfer the roast to a cutting board and carefully remove the wire rack from the skillet. Pour off any excess fat that may have accumulated during cooking, if present. Set the skillet over high heat once again and return the mushroom sauce to it, heating it until it reaches a gentle simmer. In a separate liquid measuring cup, whisk together cornstarch and water to form a slurry. Add the cornstarch mixture to the skillet, stirring constantly until the sauce thickens slightly, taking around 1 minute.\nCarve the roast into thin slices and serve it with the rich, savory mushroom sauce.