Slice the beef: Cut 3.3 lb of boneless short ribs across the grain into slices about 1/4 inch thick.
Prepare the onion: Finely grate the onion. For a cleaner marinade that burns less easily, strain the onion juice and use the liquid.
Make the marinade: Combine soy sauce, water, onion, cooking wine, sugar, honey, garlic, green onions, sesame oil, black pepper, sesame seeds, and optional ginger. Stir until well mixed.
Marinate the beef: Coat the sliced beef evenly with the marinade. Cover and refrigerate for 4–6 hours.
Grill the beef: Preheat a grill or heavy skillet over medium-high heat. Cook the beef in batches, approximately 2–4 minutes per side depending on thickness, until browned and lightly caramelized. Cook to a safe internal temperature of 145°F (63°C) with a 3-minute rest for intact beef cuts; use 160°F (71°C) for mechanically tenderized or non-intact beef if indicated by the package.
Serve: Garnish with additional sesame seeds and green onions. Serve warm with rice, kimchi, and fresh lettuce leaves.