Combine the soy sauce, brown sugar, sesame oil, rice wine or mirin, minced garlic, grated ginger, chopped green onions, sesame seeds (if using), and black pepper to create the marinade.
Place the thinly sliced beef in a shallow dish, and pour the marinade over the beef, ensuring it is evenly coated. Seal the bag or cover the dish and refrigerate for at least 1 hour, or up to 4 hours for maximum flavor.
Preheat a grill or grill pan over medium-high heat. Brush the grill with vegetable oil to prevent sticking.
Remove the marinated beef from the refrigerator and let it come to room temperature for about 10-15 minutes.
Once the grill is hot, place the marinated beef slices on the grill and cook for 2-3 minutes on each side, or until they are caramelized and cooked to your desired level of doneness.
Transfer the grilled Bulgogi to a serving platter and garnish with additional chopped green onions and sesame seeds, if desired.
Serve the Korean BBQ Bulgogi hot off the grill, either as a main dish with rice and side dishes, or wrapped in lettuce leaves with rice and dipping sauces.