In a mixing bowl, whisk together soy sauce, brown sugar, honey, gochujang, rice vinegar, sesame oil, minced garlic, and grated ginger until combined. Coat the chicken thighs in the marinade and let it marinate in the refrigerator for at least 20 minutes, or up to 2 hours.

In a large bowl, combine shredded cabbage and grated carrot. In a separate bowl, whisk together mayonnaise, sugar, salt, and black pepper. Pour the dressing over the cabbage mixture and toss to combine. Chill in the refrigerator while the chicken cooks.

Heat a cast-iron skillet or grill pan over medium-high heat and lightly oil it. Cook the marinated chicken thighs for 6-7 minutes on each side until charred and cooked through, then let it rest for 5 minutes before slicing.

Melt butter in a clean skillet over medium heat. Halve the brioche or potato buns, place them cut side down in the skillet, and toast until golden brown.

Assemble the sandwich by placing a slice of grilled chicken on each toasted bun bottom, topping with chilled cabbage slaw, and finishing with the top half of the bun.