Place the rib roast in a roasting pan and allow it to come to temperature for at least 4 hours. This will ensure it cooks more evenly.
Preheat an oven to 500 degrees F (260 degrees C).
Combine butter, pepper, and herbes de Provence in a bowl; mix until well blended. Spread butter mixture evenly over entire roast. Season roast generously with kosher salt.
Roast the 4-pound prime rib in the preheated oven for 20 minutes.
Turn the oven off and, leaving the roast in the oven with the door closed, let the roast sit in the oven for 2 hours. The roast will continue to cook during this time. Once 2 hours are up, remove roast from the oven, slice, and serve.