In a medium bowl, whisk together soy sauce, brown sugar, honey, gochujang, rice vinegar, sesame oil, minced garlic, grated ginger, and toasted sesame seeds until fully combined. Add the chicken thighs into the mixture, tossing to ensure they are well coated. Let the chicken marinate for at least 20 minutes at room temperature or refrigerate for up to 2 hours.

In a large bowl, combine shredded green cabbage, shredded red cabbage, and julienned carrot. In a separate bowl, whisk together mayo, rice vinegar, sugar, and a pinch of salt and black pepper. Pour this dressing over the cabbage mixture, tossing gently to coat. Chill until ready to assemble the sandwich.

Heat a cast-iron skillet or grill pan over medium-high heat. Add the marinated chicken thighs, cooking for about 6-7 minutes on each side until nicely charred and cooked through. Let the chicken rest for 5 minutes before slicing or serving whole.

Butter each half of the split buns and toast them cut-side down in the skillet or under the broiler until golden brown, about 2-3 minutes.

Assemble the sandwich by placing the bottom half of the toasted bun on a plate. Layer on the grilled chicken, add gochujang or Korean BBQ sauce, and top with a generous handful of the chilled slaw. Crown with the top bun and serve immediately.