Method:
Stir together tamari, brown sugar, sesame oil, half the scallions, garlic and ginger until sugar is dissolved. Put the steak in a non-reactive dish and pour the marinade over it. Turn the steak to coat the other side. Refrigerate for 30 minutes. Turn the steak and refrigerate another 30 minutes.
While steak is marinating, toast sesame seeds with ground ginger in a dry skillet over medium heat until lightly golden, 2 to 4 minutes. Remove from heat and set aside in a small bowl to cool.
Preheat the grill. When hot, oil the grill. Grill the steak a few minutes on each side, or until done to your liking. Transfer the steak to a platter, cover and let rest for a few minutes to redistribute juices. Slice steak thinly against the grain.
Transfer to a platter. Garnish with sesame seeds and remaining chopped scallions.