Heat the sesame oil in a large skillet over medium-high heat. Once hot, add the ground beef, breaking it up with a spoon as it cooks. Cook for about 5-6 minutes or until browned.

Stir in the minced garlic, diced onion, and ginger. Sauté until the onions are soft and translucent, about 2-3 minutes.

Add the soy sauce, gochujang, brown sugar (or honey), and rice vinegar to the beef mixture. Stir well to coat the beef evenly with the seasoning. Continue to cook for another 3-5 minutes, allowing the flavors to meld together. Remove from heat and sprinkle sesame seeds over the beef.

Arrange the lettuce leaves on a large plate. Start by placing a spoonful of chopped kimchi on each lettuce leaf. Then add a portion of the seasoned beef mixture on top of the kimchi, followed by a few strips of cucumber, carrot, and a sprinkle of green onions. Add an extra dollop of gochujang or Ssamjang if desired.

Garnish with more sesame seeds if you like, and serve immediately. To eat, fold the lettuce wraps like a taco, and enjoy!