Prepare the grill for indirect cooking over low heat (250° to 300°F).
Brush the oil onto both sides of the steaks and then season evenly with salt and pepper.
Grill the steaks over indirect low heat, with the lid closed, until an instant-read thermometer inserted into the center of a steak, without touching the bone, registers (100°F), 15 to 18 minutes. Transfer the steaks to a platter.
Raise the heat of the grill for direct cooking over high heat (475° to 525°F). Return the steaks to the sear grate and cook over direct high heat, with the lid closed, until an instant-read thermometer inserted into the center of a steak, without touching the bone, registers (125°F) for medium rare, 5 to 7 minutes, turning once.
Remove the steaks from the grill and let rest for about 5 minutes. Cut the meat away from the bone. Next, cut the meat across the grain into thick slices. Serve the steaks warm with the sauce.