Remove the prime rib roast from the refrigerator and allow it to come to room temperature for about 1 hour.
In a mixing bowl, combine kosher salt, black pepper, garlic powder, onion powder, smoked paprika, thyme, and rosemary. Rub the olive oil all over the prime rib and then generously apply the spice mixture, ensuring even coverage.
Preheat the smoker to a temperature of 225°F (107°C). If using a grill, set one side for indirect cooking and add wood chips to achieve smoke.
Once the smoker or grill is ready, place the prime rib on the cooking grate, bone side down. Insert a meat thermometer to monitor the internal temperature.
Smoke the prime rib at 225°F until it reaches an internal temperature of 120°F (49°C) for medium-rare, which usually takes about 3 to 4 hours. Spritz with beef broth every hour to keep the meat moist.
Once the desired temperature is reached, carefully remove the prime rib from the smoker and wrap it in aluminum foil. Allow it to rest for 20-30 minutes.
After resting, unwrap the roast and slice against the grain. Serve with your favorite sides.