In a blender or small food processor, combine the soy sauce, olive oil, garlic, brown sugar, vinegar, and ginger. Puree until smooth.
Place the flank steak in a shallow dish just large enough to hold it. With a skewer or kitchen fork, pierce the steak many times. Pour the soy mixture over the meat. Cover and refrigerate, turning and piercing the steak again every hour, for 8 hours. Return to room temperature.
Light a hot fire in a charcoal grill or preheat a gas grill or grill pan to medium-high heat.
Grill steak on an oiled rack set 5 to 6 inches over glowing coals or in grill pan for 5 minutes on each side for medium-rare meat.
Transfer steak to a cutting board and let stand for 10 minutes. Holding a sharp knife at a 45 degree angle, cut steak across the grain into very thin slices