Combine soy sauce, ketchup, green onions, and dark sesame oil in a large zippered plastic bag.
Place beef steak in the bag with marinade, seal, and mix well to coat all sides. Refrigerate for at least 4 hours, preferably overnight.
Preheat grill to medium-high heat. Grease the grill grate with vegetable oil. Remove marinated steak from bag and place on grill. Cook for 6 minutes on each side, or until internal temperature reaches 60°C (140°F) for medium doneness.
Transfer steak to a cutting board and let rest for 5 minutes. Cut into slices across the grain. Serve immediately and garnish to taste.