Cut the beef slices into strips about an inch wide. Place in a bowl with the vegetables.
Stir together all the ingredients for the marinade. Pour over the beef and vegetables. Cover the bowl and leave to marinate in the fridge for at least six hours or overnight.
Heat your grill or skillet. Optionally, brush with oil.
Drain the beef and vegetables. Spread on the hot grill or skillet and cook until the underside is nicely browned, about two to three minutes. Using a wide spatula, scoop and flip to brown the opposite side for about two minutes. Stir around for another minute or two to make sure that the beef is cooked through.
Sprinkle the bulgogi with toasted sesame seeds before serving.