Bring to room temperature. Remove the prime rib from the fridge 2 to 3 hours before cooking, and allow it to come to room temperature.
Make the herb butter. Preheat your oven to 450°F (230°C). In a small bowl, mix together the butter, garlic, salt, thyme, rosemary, and black pepper.
Coat the prime rib. After the prime rib has come to room temperature, pat it down with paper towels to make sure it's dry. Then, rub the entire outside of the prime rib with the herb butter mixture.
Prep the prime rib. Place the prime rib in an oven-safe pan or roasting tray with the bone-side down, fat-side up. If you're making the red wine au jus, place the onion slices in the pan around the meat. If not, you can omit the onions.
Cook the prime rib. Cook the prime rib in the center of the oven for 20 minutes at 450°F (230°C). It should get a nice sear on the outside. If it doesn't have much of a crust, cook it a few minutes longer. Then, reduce the temperature to 325°F (160°C) and continue cooking the prime rib until the internal temperature reaches 120°F (50°C). This should take about an hour and a half for medium-rare. Note: go by temperature (listed above), and not time, as it will depend on the size of your prime rib and your oven.
Let it rest. Remove the prime rib from the oven and let it rest for 20 to 30 minutes. You can tent it with aluminum foil to keep it warm. Then, remove the string and bones, and slice it up into thick ½-inch thick slices.