Place chicken wings in a 1 gallon sealable plastic bag set in a shallow dish.
Stir together the 1/4 cup green onion, soy sauce, brown sugar, sesame oil, ginger, and garlic. Pour marinade over wings. Close bag. Marinate in the refrigerator for 2 to 24 hours, turning occasionally.
Drain wings and pour the marinade into a saucepan. Bring the marinade to a boil and immediately remove from heat; set aside to cool. Divide marinade using one half to baste the wings as they cook. Serve the remaining half as a dipping sauce.
Place wings on a lightly oiled rack on the grill directly over medium heat. Grill for 15 to 20 minutes turning and basting frequently. (Wings can also be broiled for 10 to 15 minutes until they've browned.)
Sprinkle with sesame seeds, chopped green onion and reserved dipping sauce.