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 blended. Toss the boneless skinless chicken thighs into the marinade, ensuring each piece is thoroughly coated. Let the chicken marinate for at least 20 minutes at room temperature, or for deeper flavor, refrigerate for up to 2 hours.

In a large bowl, combine the shredded green and red cabbage along with the julienned carrot. In a separate smaller bowl, whisk together mayonnaise, rice vinegar, sugar, salt, and black pepper until smooth. Pour this dressing over the cabbage mixture and toss well to coat. Cover and chill the slaw in the refrigerator until you're ready to assemble.

Heat a cast-iron skillet or grill pan over medium-high heat, lightly oiling the surface if necessary. Once hot, add the marinated chicken thighs, cooking for about 6-7 minutes on each side, or until they are nicely charred and cooked through. Let the chicken rest for 5 minutes before slicing or leaving whole for your sandwich.

While the chicken is resting, split the brioche or potato sandwich buns and lightly butter each half. Place the buns cut-side down on the hot skillet or under a broiler. Toast them until golden brown and crisp on the edges, which should take about 2-3 minutes, being careful not to burn them.

Begin assembling your Korean BBQ Chicken Sandwich with the toasted bottom bun. Place sliced or whole grilled chicken on the bun, then generously spoon on some extra BBQ sauce or a Korean BBQ sauce dip for added flavor. Top it off with a heaping helping of the chilled cabbage slaw, and crown it all with the top bun. Serve hot and savor the explosion of flavors!