Preheat your oven to 450°F (230°C). Pat the prime rib roast dry with paper towels. Season generously with salt and pepper on all sides.

In a large oven-safe skillet or roasting pan, heat the olive oil over medium-high heat. Once hot, add the prime rib roast and sear on all sides until browned, about 3-4 minutes per side.

Remove the roast from the pan and set aside. In the same pan, add the minced garlic, chopped rosemary, and thyme. Sauté for 1-2 minutes until fragrant.

Pour in the balsamic vinegar and scrape up any browned bits from the bottom of the pan. Let it simmer for 2-3 minutes until slightly reduced.

Stir in the beef broth and add the chopped root vegetables. Return the prime rib to the pan, placing it on top of the vegetables.

Cover the pan tightly with aluminum foil or a lid. Transfer to the preheated oven and roast for 15 minutes. Lower the temperature to 325°F (160°C) and continue cooking for about 2-3 hours, or until the internal temperature reaches your desired doneness (125°F for rare, 135°F for medium-rare).

Remove the prime rib from the oven and let it rest for at least 20-30 minutes before slicing to allow the juices to redistribute.

If you prefer a thicker gravy, remove the vegetables and liquid from the pan and bring to a simmer. Mix cornstarch with a little cold water to create a slurry and stir it into the simmering liquid until thickened.

Slice the prime rib and serve it with the root vegetables and rich gravy. Garnish with fresh herbs if desired.