Press the chicken thighs between parchment paper using a tortilla press until thin, wide, and evenly flattened. Season lightly with salt.

Whisk together buttermilk, hot sauce, and salt. Add the pressed chicken and marinate for at least 30 minutes, or up to overnight for deeper flavor.

In a shallow bowl, combine flour, potato starch, salt, and black pepper. Remove chicken from the marinade and firmly press into the dredge, squeezing to create craggy edges for extra crispy fried chicken texture. Let the coated chicken rest for 10 minutes before frying.

Heat neutral oil to 350°F (175°C). Fry chicken for 5 to 7 minutes, or until golden brown, crispy, and cooked through. Drain on a wire rack.

In a heatproof bowl, combine gochujang, Korean chili flakes, garlic powder, soy powder or soy sauce, MSG, Dijon mustard, and rice wine vinegar. Carefully ladle 4 to 6 ounces of hot fryer oil into the bowl and whisk until glossy and emulsified. Toss fried chicken in the Korean fried chicken sauce until fully coated.

In a large bowl, combine shaved Napa cabbage, scallions, and cucumber. In a separate bowl, mix Kewpie mayonnaise, sambal, and kimchi base. Fold the dressing into the vegetables and chill until ready to assemble.

Heat a skillet over medium. Place brioche buns cut side down and generously cover both the buns and surrounding skillet with shredded Jack cheese. Let the cheese melt and spread to create crispy cheese skirts. Place sauced chicken on the bottom bun halves and transfer the skillet to a 400°F (205°C) oven for 4 to 5 minutes until fully melted.

Top the chicken with kimchi slaw, close the sandwich, press gently, slice in half, and serve immediately.