In a large mixing bowl, blend soy sauce, brown sugar, honey, gochujang, rice vinegar, sesame oil, minced garlic, and grated ginger. Add chicken thighs, ensuring they are fully coated. Let them marinate for at least 20 minutes, preferably 2 hours.

In another bowl, combine shredded green and red cabbage with grated carrot. In a separate bowl, whisk mayonnaise, rice vinegar, sugar, salt, and pepper. Pour over cabbage mixture, mixing well, then chill until ready to serve.

Preheat your grill pan over medium-high heat. Lightly oil the pan and add marinated chicken. Grill for 6-7 minutes per side, or until nicely charred and cooked through. Allow the chicken to rest for 5 minutes before slicing.

Cut each sandwich bun in half and spread butter on both sides. Toast in the same skillet or on the grill until golden brown.

Assemble the sandwich with the bottom bun, layer with sliced grilled chicken, BBQ sauce, and top with chilled cabbage slaw. Finish with the top bun and serve immediately.