Marinate the tuna in this mixture in the refrigerator for at least 30 minutes, two hours or more is ideal. If you can, remove the tuna from the fridge twenty minutes before cooking so it can come to room temperature.
When ready to cook, remove the tuna from the marinade, brushing off any green onions. Brush the grill with oil or spray with cooking spray. Cook the tuna for about 2 minutes on each side for medium rare. For medium well, cook about 4 minutes on each side.