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

While the chicken marinates, prepare the slaw. In a large bowl, combine the shredded green cabbage, red cabbage, and carrot. In a small bowl, whisk together the mayonnaise, rice vinegar, sugar, salt, and pepper. Pour the dressing over the cabbage mixture and toss well to coat. Refrigerate until serving to keep it crisp and cool.

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

Let the cooked chicken rest for 5 minutes before slicing against the grain or serving whole on the sandwich.

Split the buns and spread the cut sides lightly with 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 on the sliced or whole grilled chicken, drizzle with extra gochujang or Korean BBQ sauce if desired, then top with a generous handful of the chilled cabbage slaw. Crown with the top bun and serve immediately.