Cut chicken breasts in half and place in large mixing bowl. Cover with buttermilk and sprinkle liberally with salt and pepper. Place bowl in refrigerator to marinate. Ideally the chicken will marinate for at least an hour, but in a pinch as little as 5 minutes will work.
Add enough oil to a large cast iron skillet until it's about 1" deep. Cast iron is best for frying the chicken until it's brown and crisp because it heats so evenly, but a heavy dutch oven will work as well. Heat oil over medium high heat until an instant read thermometer reads about 350 degrees.
Using a fork, remove chicken pieces one at a time from buttermilk, and dredge in flour. Sprinkle off the excess flour and place in oil gently, making sure to lay it away from yourself to avoid splatters. If your skillet won't hold all the chicken, work in batches. Crowding the skillet will result in soggy, greasy chicken.
When chicken is brown and crispy, remove to a rack set over a baking sheet and test temperature with an instant read thermometer. The internal temperature should be 165 degrees. Sprinkle with salt.
COLESLAW
While the chicken is marinating (or frying) make the coleslaw. In a medium bowl, combine vinegar, honey, olive oil, allspice, salt and pepper. Using a whisk or a fork, combine well.
Add coleslaw mix, radishes, onions and pickled peppers to dressing and mix well to combine.
ASSEMBLY
Cut buns in half and spread mayonnaise on bottom. Add chicken, cheese and coleslaw. Add top bun and enjoy!