Marinate the Chicken: Whisk together soy sauce, brown sugar, honey, gochujang, rice vinegar, sesame oil, garlic, and ginger. Add chicken thighs, coat well, cover, and refrigerate for at least 20 minutes.

Prepare the Cabbage Slaw: Mix green and red cabbage with julienned carrot. In another bowl, whisk mayonnaise, remaining rice vinegar, and optional sugar. Combine with cabbage, toss, and chill for at least 15 minutes.

Cook the Chicken: Heat a skillet over medium-high heat. Cook marinated chicken thighs for 6-7 minutes on each side until cooked through. Let rest for 5 minutes.

Toast the Buns: Melt butter in the skillet and toast buns cut side down until golden brown.

Assemble the Sandwich: Slice chicken, layer on the bottom half of each toasted bun, add Korean BBQ sauce if desired, top with slaw, and cover with the other bun half.