In a medium bowl, whisk together the soy sauce, brown sugar, honey, gochujang, rice vinegar, sesame oil, minced garlic, grated ginger, and toasted sesame seeds. Add the chicken thighs and toss to coat thoroughly. Let the chicken marinate at room temperature for at least 20 minutes, or refrigerate for up to 2 hours for deeper flavor.

While the chicken marinates, prepare the slaw. In a large bowl, combine the shredded green and red cabbage with the shredded carrot. In a small bowl, whisk together the mayonnaise, rice vinegar, sugar, salt, and pepper. Pour the dressing over the cabbage mixture and toss to coat evenly. Cover and refrigerate until ready to serve, allowing the flavors to meld.

Heat a cast-iron skillet or grill pan over medium-high heat. Lightly oil the pan if needed. Add the marinated chicken thighs and cook for 6-7 minutes on each side, until nicely charred and cooked through (internal temperature reaches 165°F). The sugars in the marinade will caramelize for a beautiful crust.

Transfer the cooked chicken to a cutting board and let rest for 5 minutes before slicing or serving whole.

Spread the cut sides of the buns lightly with softened butter. Toast them in the same skillet or under the broiler until golden and crisp on the edges, about 1-2 minutes. This prevents sogginess and adds texture.

Place the bottom bun on a plate. Layer with sliced or whole grilled chicken, then spoon on any extra Korean BBQ sauce or gochujang if desired. Top with a generous handful of the chilled cabbage slaw. Crown with the top bun and serve immediately.