For the mayonnaise: Whisk together the mayonnaise, gochujang, lime zest and some salt and pepper in a bowl, cover and refrigerate to allow the flavors to meld, at least 30 minutes.
For the slaw: Whisk together the vinegar, soy and honey in a large bowl until combined. Add the cabbage, kimchee and cilantro. Season with salt and pepper, and then toss to combine. Cover and let sit at room temperature for at least 30 minutes to allow flavors to meld.
For the chicken: Preheat the oven to 325 degrees F. Heat the oil in large Dutch oven or a deep fryer until a deep-frying thermometer inserted into the oil reaches 365 degrees F.
Divide the flour between 2 large shallow bowls and season each with salt and pepper. Whisk together the coconut milk, buttermilk, ginger and garlic in a large shallow bowl and season with salt and pepper. Set up your breading station: flour, milk, flour.
Dredge the chicken in the flour and tap off any excess. Dip in the milk mixture and let any excess drip off. Dredge in the second bowl of flour and tap off any excess. Fry the chicken, in batches, until golden brown and cooked through, 4 to 5 minutes. Remove to a baking sheet fitted with a baking rack. Repeat with the remaining chicken. Place in the oven to crisp up, about 5 minutes.
Spread some mayo on each side of the buns. Top with a chicken breast and finish with some of the slaw, then serve.