Prepare the Roast: Pat the prime rib roast dry with paper towels. Rub the entire roast with olive oil, ensuring an even coating.

Season the Roast: In a small bowl, combine minced garlic, chopped rosemary, chopped thyme, kosher salt, and black pepper. Rub this herb mixture evenly over the surface of the roast, pressing gently to adhere.

Sear the Roast: Heat a large skillet over medium-high heat. Place the seasoned roast in the hot skillet and sear each side until browned, approximately 2-3 minutes per side. This step enhances the flavor by creating a savory crust.

Prepare the Slow Cooker: Transfer the seared roast to the slow cooker. Pour the beef broth into the slow cooker, around the sides of the roast to avoid washing away the seasoning.

Cook the Roast: Cover the slow cooker with its lid. Set it to cook on low heat for 3 to 5 hours, depending on your desired level of doneness. For medium-rare, aim for an internal temperature of 130°F (54°C); for medium, 140°F (60°C). Use a meat thermometer to check the temperature, inserting it into the thickest part of the roast.

Rest the Roast: Once the desired internal temperature is reached, remove the roast from the slow cooker and place it on a cutting board. Tent it loosely with aluminum foil and allow it to rest for 20 minutes. This resting period lets the juices redistribute throughout the meat, resulting in a moist and tender roast.

Prepare the Horseradish Sauce: While the roast rests, in a small bowl, mix together sour cream, prepared horseradish, Dijon mustard, and chopped chives. Season with salt and freshly ground black pepper to taste. Stir until well combined.

Serve: After resting, slice the prime rib roast against the grain into desired thickness. Serve with the horseradish sauce on the side.