In a large bowl, whisk together soy sauce, brown sugar, honey, gochujang, rice vinegar, sesame oil, minced garlic, and grated ginger until smooth. Add the chicken thighs, ensuring they are fully coated in the marinade. Cover and refrigerate for at least 20 minutes, or up to 2 hours for deeper flavor infusion.

Heat a skillet over medium-high heat and add a splash of oil if desired. Once hot, add the marinated chicken thighs, cooking for about 6-7 minutes per side until browned and reaching an internal temperature of 165°F (75°C). Let the chicken rest for a few minutes before slicing.

While the chicken marinates, shred both green and red cabbage, and julienne or grate the carrot. In a separate bowl, whisk together mayonnaise, rice vinegar, sugar, salt, and black pepper until smooth. Toss this mixture with the cabbage and carrot, combining well, then chill the slaw until ready to assemble.

To build your Korean BBQ Chicken Sandwich, layer sliced chicken on the bottom half of each toasted bun. If desired, drizzle some extra BBQ sauce over the chicken for added flavor. Top generously with the prepared crunchy slaw, and place the other half of the bun on top.