- Preheat the grill, setting the burners to high. Oil the grate.
- Trim visible fat from the beef. Grill for about 3 minutes on each side for rare meat, or until the desired doneness. Let rest for 5 minutes. Season with salt and pepper.
- In a dish or a large sealable plastic bag, combine the marinade ingredients. Add the cooled, whole steaks. Cover the dish or seal the bag. Refrigerate for 8 hours. Turn occasionally.
- Cut the steaks into thin strips. Arrange on a plate, garnish with arugula and drizzle with the marinade. Serve with lime wedges, if desired.