In a large bowl, combine the soy sauce, brown sugar, minced garlic, grated ginger, sesame oil, and red pepper flakes. Stir until the sugar is dissolved. Add the thinly sliced beef sirloin and toss to coat evenly. Let it marinate for at least 15 minutes.
While the beef marinates, chop the kimchi into bite-sized pieces. In a separate bowl, mix the chopped kimchi, shredded carrots, sliced green onions, and rice vinegar. Toss everything together until well combined. Set aside.
Heat a skillet or grill pan over medium-high heat. Add the marinated beef in a single layer and cook for 2-3 minutes per side until cooked through and caramelized. Cook in batches if necessary.
Warm the corn tortillas on a dry skillet or over an open flame for a few seconds on each side until pliable.
Place slices of the sticky Korean BBQ beef onto each warm tortilla. Top generously with kimchi slaw and sprinkle with sesame seeds. Serve immediately.
