Stir soy sauce, sugar, scallions, sesame oil, sesame seeds, garlic and ginger together in a bowl. Fold the flank steak into thirds. Place in a large resealable plastic food storage bag. Pour the soy sauce and brown sugar mixture into the bag. Seal bag and turn over to cover steak. Place in refrigerator for two hours.
Heat grill or broiler. Remove steak from bag. Place marinade in small saucepan and bring to a boil. Reduce heat and simmer 5 minutes.
Grill or broil steak for 5 minutes per side or until meat registers 135 degrees.
Allow meat to rest for 5 minutes before slicing.