For the sauce: In the work bowl of a food processor, combine all the sauce ingredients. Pulse until the mixture is finely chopped. Transfer the mixture to a medium bowl. Cover and refrigerate up to 3 days.
For the steaks: Spray the grill rack with nonstick, nonflammable cooking spray. Preheat the grill to medium-high heat.
Brush both sides of the steaks evenly with oil. Sprinkle with salt and pepper. Grill the steaks for 5 minutes per side, or to desired degree of doneness. Remove the steaks from the grill and let stand for 5 minutes. Serve with the garlic parsley sauce.