In a small bowl, whisk together soy sauce, sesame oil, rice vinegar, garlic, ginger, green onions, and black pepper.
Add the beef and let it marinate for at least 30 minutes.
Heat a skillet over medium-high heat.
Add the beef and cook until browned and slightly caramelized, about 5 minutes.
In a small bowl, stir together gochujang, miso paste, sesame oil, rice vinegar, garlic, and green onion until smooth.
Place beef into lettuce leaves.
Add cucumber sticks, pickled radish, and carrot matchsticks.
Top with kimchi if using.
Drizzle with sauce and sprinkle with toasted sesame seeds.
Wrap, fold, and enjoy immediately.