1. Preheat one side of a gas grill to high and the other to medium. Or build a large fire in a charcoal grill and arrange the coals so that you have a hot side and a cooler side.
2. Season the steaks liberally with salt and black pepper, then rub in the olive oil. Put the steaks on the grill and cook for 10–12 minutes, until both sides are a rich mahogany brown. Transfer to the cooler part of the grill to cook for another 5 minutes.
3. For the seasoned butter, combine all of the ingredients in a food processor or blender. Purée until well mixed. To serve the steaks, transfer to a large platter and top each steak with a heaping teaspoon of the seasoned butter which will slowly melt over the steaks.