In a medium bowl, whisk together soy sauce, brown sugar, honey, gochujang, rice vinegar, sesame oil, minced garlic, and grated ginger until well combined. Add the chicken thighs and coat well. Refrigerate for at least 20 minutes.

In a large mixing bowl, combine shredded green and red cabbage with the julienned carrot. In a separate small bowl, whisk together mayonnaise, a splash of rice vinegar, sugar, salt, and pepper until smooth. Pour over the cabbage mixture and toss. Chill until ready.

Preheat a skillet or grill pan over medium-high heat for about 5 minutes. Remove marinated chicken, let excess marinade drip off, and cook for approximately 6–7 minutes on each side until browned and cooked through. Allow to rest for 5 minutes before slicing.

Spread butter on the cut sides of the buns. Toast them cut-side down in the skillet for about 2–3 minutes until golden and crisp.

Assemble the sandwich by laying sliced chicken on the bottom half of each bun, drizzling with BBQ sauce if desired, and topping with crunchy slaw. Place the other half of the bun on top and serve immediately.