In a medium bowl, combine soy sauce, sesame oil, brown sugar, minced garlic, grated ginger, rice vinegar, black pepper, and red pepper flakes. Stir well until the brown sugar dissolves completely and the marinade is smooth.
Add the thinly sliced beef sirloin to the marinade, ensuring each piece is well coated. Cover the bowl with plastic wrap or transfer everything into a resealable plastic bag. Let it marinate in the refrigerator for at least 30 minutes, or up to 2 hours for more intense flavor.
While the beef marinates, wash and separate the butter lettuce leaves carefully, keeping them whole and intact. Shred the carrots, slice the cucumbers thinly, and chop the green onions. Set these aside for assembling the wraps later.
Heat a large skillet or grill pan over medium-high heat. Once hot, add the marinated beef in a single layer. Cook for 2-3 minutes per side or until the beef is nicely browned and cooked through. Avoid overcrowding the pan—cook in batches if necessary. Remove from heat.
In a small dry skillet, toast the sesame seeds over medium heat for 2-3 minutes until golden and fragrant. Stir frequently to prevent burning. Remove from heat and set aside.
Lay out a butter lettuce leaf on a plate. Add a few slices of cooked beef, then top with shredded carrots, sliced cucumbers, and chopped green onions. Sprinkle with toasted sesame seeds for a nutty finish. Fold the lettuce leaf around the fillings and enjoy immediately.