In a small mixing bowl, whisk together the gochujang, soy sauce, sesame oil, ginger, garlic, brown sugar, and rice vinegar until smooth.
Place the chicken thighs in a large bowl and coat with two-thirds of the gochujang mixture; reserve the remaining third for glazing.
Allow the chicken to marinate for a minimum of 20 minutes at room temperature.
In a separate bowl, combine the shredded cabbage, mayonnaise, and sesame seeds to create the slaw.
Preheat a cast-iron grill pan or outdoor grill to medium-high heat (approximately 400°F/204°C).
Place chicken on the grill and cook for 5 to 7 minutes per side, or until the internal temperature reaches 165°F (74°C).
During the final 2 minutes of grilling, brush the reserved sauce onto the chicken to create a caramelized glaze.
Lightly toast the brioche buns until golden brown.
Assemble by spreading a thin layer of mayonnaise on the bottom bun, followed by the grilled chicken, a generous portion of sesame slaw, chopped kimchi, and sliced green onions.
Close the sandwich and serve immediately.