Prepare grill according to manufacturer's instructions.
Place onion on baking sheet; brush both sides lightly with oil and season with salt and pepper.
Sprinkle both sides of steak with salt and pepper. Place onion and steak directly on grill. Grill onion, turning once, until streaked with dark grill marks, 10 to 12 minutes. Grill steak until well seared and dark brown on side, 5 to 7 minutes. Using tongs, flip steak; continuing grilling on other side until interior of meat is slightly less done than you want it to be when you eat it, 2 to 5 minutes more for rare or medium-rate.
Transfer steak to cutting board, cover loosely with foil and let rest for 5 minutes. Slice steak very thing on bias against the grain. Season with salt & pepper to taste. Place onions on platter and arrange meat over onions. Serve with Chimichurri Sauce.
For Chimichurri Sauce:
Process parsley and garlic in the work bowl of a food processor fitted with a steel blade, stopping as necessary to scrape sides of bowl. Until ingredients are chopped fine. Transfer mixture to medium bowl. Whisk in oil, vinegar, pepper flakes, salt and 2 tablespoons water until thoroughly blended. Serve immediately.