In a mixing bowl, combine the soy sauce, brown sugar, sesame oil, minced garlic, grated ginger, red pepper flakes, and black pepper. Whisk until the sugar is dissolved and the ingredients are well mixed.
Heat your large skillet over medium-high heat. Add the lean ground beef and cook until browned, breaking it apart with a spatula as it cooks. This should take about 5-7 minutes.
Once the beef is cooked through, drain any excess fat if necessary. Pour the sauce over the beef, stirring well to coat the meat evenly. Allow it to simmer for an additional 2-3 minutes until the sauce thickens slightly.
While the beef is simmering, prepare your fresh vegetables. Rinse and slice the cucumber, red bell pepper, and chop the green onions. Set aside the shredded carrots as well.
To serve, arrange the lettuce leaves on a serving platter. Spoon a portion of the beef mixture into the center of each leaf, and top with shredded carrots, cucumber, red bell pepper, and green onions. Sprinkle sesame seeds on top if desired.
Fold the lettuce leaf around the filling like a taco, and enjoy your Korean Lettuce Wraps!