Season all sides of the rib-eyes liberally with salt and pepper. Place on wire rack-lined baking sheet. Bake until the desired internal temperature is reached, 105 degrees F for rare, 115 for medium rare and 125 for medium, 1 1/2 to 2 hours. When the rib-eyes come out of the oven, tent loosely with aluminum foil while preheating the skillet.
Heat a cast-iron skillet over medium-high heat. Add the oil, then sear the steaks on the first side for about a minute. Flip the steaks and add the butter to the skillet. Once the butter has melted, continue to cook the steaks, continuously basting with the melted butter, until seared on the second side, about 45 seconds. Sear the fat cap as well to crisp up, 30 seconds to 1 minute.
Slice and serve immediately, spooning the pan juices over each slice. There is no need to rest the meat with the reverse sear method.