Combine first 9 ingredients in a bowl, stirring until sugar dissolves. Reserve 1/3 cup marinade. Pour remaining marinade into a large zip-top plastic bag. Add meat, and marinate in refrigerator 8 hours, turning bag occasionally.
Remove meat from bag; discard marinade from bag. Place meat on a broiler pan coated with cooking spray. Broil 6 to 8 minutes per side. Let stand 5 minutes.
Place reserved 1/3 cup marinade in a small saucepan. Cook over medium heat 2 to 3 minutes or until hot.
Cut steak diagonally across grain into thin slices. Serve over Spicy Cabbage; drizzle with reserved marinade.