In a mixing bowl, whisk together soy sauce, brown sugar, honey, gochujang, rice vinegar, sesame oil, minced garlic, grated ginger, and sesame seeds until well combined. Coat the chicken thighs in this marinade and let sit for at least 20 minutes (up to 2 hours in the refrigerator for deeper flavor).

In a large bowl, combine the shredded green cabbage, red cabbage, and julienned carrot. In a smaller bowl, whisk together mayonnaise, rice vinegar, sugar, salt, and pepper until smooth. Pour over cabbage mixture, toss until coated, and refrigerate.

Heat a skillet or grill pan over medium-high heat. Add marinated chicken and cook for 6-7 minutes on each side until charred and internal temperature reaches 165°F. Remove from heat, let rest for 5 minutes before slicing.

Butter the inside of each sandwich bun and toast cut-side down in the skillet or under a broiler until golden and crispy, about 2-3 minutes.

Assemble the sandwich: Start with a toasted bottom bun, layer with sliced grilled chicken, drizzle additional Korean BBQ sauce, and top with cabbage slaw. Add the top bun and serve immediately.