In a mixing bowl, combine soy sauce, brown sugar, honey, gochujang, rice vinegar, sesame oil, garlic, and ginger. Whisk until blended, then add chicken and marinate for at least 20 minutes or up to 2 hours.

In a large bowl, mix cabbage with carrots. In a separate bowl, whisk together mayonnaise, rice vinegar, sugar, and season with salt and pepper. Combine with cabbage mixture and chill for 15 minutes.

Heat the grill pan over medium-high heat. Cook marinated chicken for 6-7 minutes per side until internal temperature reaches 165°F. Transfer to a plate and let rest before slicing.

Spread butter on the cut sides of the buns and toast in a non-stick skillet over medium heat until golden brown.

Assemble the sandwich by layering sliced chicken on the bottom bun, drizzle with remaining marinade if desired, top with cabbage slaw, and add the top bun.