Trim steak, if necessary, and cut into 2-inch medaillons.
Stir together balsamic vinegar and next 7 ingredients in a large, shallow dish or zip-top plastic freezer bag; add medaillons, turning to coat. Cover or seal, and chill 8 hours, turning once after 4 hours.
Remove medaillons from marinade, discarding marinade. Place on a lightly greased wire rack in a heavy-duty aluminum foil-lined roasting pan.
Broil 6 inches from heat 6 to 8 minutes on each side or to desired degree of doneness. Remove steaks from oven, and let stand 5 minutes.