Pound the steaks on both sides, using a mallet, until 1/4-inch thin. Season with garlic, lime juice, salt & pepper. Allow to marinate at least 1 hour, refrigerated.
Remove the steaks from marinade & pat dry. In a large frying pan, heat the oil over medium heat until very hot. Brown each steak for 2 to 3 minutes on each side.
Transfer the steaks to a serving platter & keep warm. Add the marinade & onion to the pan & cook until the onion is slightly wilted, 3 to 4 minutes. Garnish the steaks with the onion & parsley & serve immediately.