Prepare Beef: Place the steak in the freezer for 30 minutes to firm up slightly. Then, using a sharp knife, slice the steak thinly against the grain.
Marinate: In a large bowl, mix the sliced steak with dark soy sauce, gochujang paste, minced ginger, light brown sugar, mirin, minced garlic, black pepper, grated apple, and toasted sesame oil. Cover and refrigerate for 3-4 hours.
Cook Beef: Heat the neutral oil in a large frying pan over medium-high heat. Use a slotted spoon to scoop out the steak from the marinade, allowing excess sauce to drip off. Fry the steak in the hot oil, using tongs to separate the slices. Cook for approximately 5 minutes, until the beef is cooked through and caramelized.
Assemble Wraps: Place the lettuce leaves on a large platter. Fill each with bulgogi beef, carrot, cucumber, bell peppers, and spring onions. Sprinkle with sesame seeds and chopped peanuts if desired.
Serve: Serve the lettuce rolls immediately, optionally adding a spoonful of cooked rice to each wrap for a more substantial meal.