Add all ingredients to a small food processor or blender. Pulse until mixture is fairly smooth but not pureed.
Preheat grill or grill pan over high heat for 5-10 minutes. Brush steak on both sides with oil. Sprinkle generously with salt and pepper. Grill steak until well seared on bottom. Don't attempt to flip it until it releases easily when you gently lift a corner with tongs. When the bottom is nicely seared with beautiful grill marks, flip and finish cooking on the other side until internal temperature reaches 125ºF for medium rare. Transfer steak to a cutting board, tent with foil and let it rest for 5 minutes to redistribute the juices before slicing. Serve steak sliced with green sauce drizzled over.