In a medium bowl, whisk together soy sauce, brown sugar, honey, gochujang, rice vinegar, sesame oil, garlic, ginger, sesame seeds, and green onions.
Add the chicken and toss until fully coated. Marinate for 20 minutes at room temperature or refrigerate for up to 2 hours.
Prepare the slaw by combining green cabbage, red cabbage, and carrot in a large bowl.
In a separate bowl, whisk together mayonnaise, rice vinegar, sugar, salt, and pepper.
Pour the dressing over the vegetables and toss until evenly coated. Refrigerate until ready to serve.
Heat a cast-iron skillet or grill pan over medium-high heat.
Cook the marinated chicken for 6–7 minutes per side, or until caramelized and cooked through to an internal temperature of 165°F (74°C).
Transfer the chicken to a cutting board and let it rest for 5 minutes before slicing.
Lightly butter the buns and toast them until golden brown.
Assemble the Korean BBQ Chicken Sandwich by placing the chicken on the bottom bun, adding extra sauce if desired, topping generously with cabbage slaw, and finishing with the top bun.
Serve immediately while warm.