In a glass dish or a sealable plastic bag, coat the flank steaks with 1 1/2 cup (375 ml) chimichurri sauce. Cover the dish or seal the bag and refrigerate for 12 to 24 hours. In a bowl, combine all the ingredients. Refrigerate the remaining sauce until ready to serve.
Preheat the grill, setting the burner to high. Oil the grate.
Drain the flank steaks and discard the marinade. Rub the meat with salt and pepper. Grill the steaks for about 5 minutes on each side for rare meat, or until the desired doneness. Let rest for 5 minutes.
Slice into thin strips against the grain of the meat and drizzle with the remaining chimichurri sauce. If desired, serve with rice and avocado slices drizzled with lime juice.