In a medium bowl, whisk together soy sauce, brown sugar, honey, gochujang, rice vinegar, sesame oil, minced garlic, grated ginger, and toasted sesame seeds until the sugar dissolves.

Add the chicken thighs and toss well to coat each piece. Let them marinate at room temperature for 20 minutes, or cover and refrigerate up to 2 hours for deeper flavor.

In a large bowl, combine the shredded green cabbage, red cabbage, and grated carrot.

In a small bowl, whisk together mayonnaise, rice vinegar, sugar, salt, and pepper. Pour the dressing over the cabbage mixture and toss until evenly coated. Refrigerate until ready to serve.

Heat a cast-iron skillet or grill pan over medium-high heat. Lightly oil the pan if needed. Place the marinated chicken thighs in the pan and cook for 6-7 minutes per side, until nicely charred and cooked through (internal temperature reaches 165°F).

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

Split the buns in half and spread the cut sides with softened butter. Toast them in the same skillet over medium heat, cut side down, until golden and crisp, about 1-2 minutes. Alternatively, toast under the broiler.

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