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 well combined. Add the boneless skinless chicken thighs, ensuring they are thoroughly coated in the marinade. Allow the chicken to marinate for at least 20 minutes at room temperature, or for a more intense flavor, refrigerate for up to 2 hours.

In a large bowl, combine the shredded green cabbage, red cabbage, and julienned carrot. In a separate small bowl, whisk together the mayonnaise, rice vinegar, sugar, salt, and pepper until smooth. Pour the dressing over the cabbage mixture and toss until everything is evenly coated. Cover and chill the slaw in the refrigerator while you cook the chicken, allowing the flavors to meld.

Heat a cast-iron skillet or grill pan over medium-high heat. If desired, lightly oil the skillet to prevent sticking. Add the marinated chicken thighs, cooking them for 6-7 minutes on each side until they are nicely charred and no longer pink in the center. Once cooked through, remove the chicken from the heat and let it rest for 5 minutes before slicing.

While the chicken is resting, split the brioche or potato sandwich buns in half and lightly butter each half with softened butter. Place the buns on the skillet or under the broiler for a few minutes, toasting them until golden brown and crisp around the edges. Keep an eye on them to prevent burning, as they toast quickly.

To assemble your Korean BBQ Chicken Sandwich, layer the sliced or whole grilled chicken on the bottom half of each toasted bun. Drizzle extra BBQ sauce or a gochujang dip on top, if desired, to enhance the flavor. Then, add a generous handful of the chilled cabbage slaw over the chicken. Crown with the top bun, and your delicious sandwich is ready to serve hot!