Salt steaks generously on both sides and let come to room temperature, about 30 minutes.
In a medium bowl, combine Worcestershire sauce, vinegar, ketchup, and brown sugar and mix well until sugar has dissolved.
Heat grill to medium (350° to 450°). Blot steaks dry. Brush sauce on one side of the steaks. Place steaks, sauce side down, on grate and cook for 2 minutes. Brush the top of the steaks with sauce, and turn over. Cook 2 minutes more. Brush the top of the steaks with sauce again, turn, and cook for 2 minutes. Brush the top of the steaks, turn, and cook for the final 2 minutes. Steaks should be deep brown and cooked to an internal temperature of 125° on an instant-read thermometer for medium rare. Let steaks rest for 10 minutes. Slice into 1⁄4-in. pieces and serve.