Chicken Cordon Bleu is typically made by stuffing the ham and cheese inside the breast, but for the sake of this sandwich–don't worry about it! Stacking the ham and cheese on top the buns, popping it in the broiler, then adding fried chicken works perfectly and cuts your prep time (and potential mess-ups) in half!
Begin by brining the chicken. Add the chicken and buttermilk to a ziplock bag and refrigerate. As for time, it's best if the chicken stays in the buttermilk for 48 hours, but overnight will work too.
Once the chicken has soaked up the buttermilk, it's time to fry. Heat enough oil to cover the chicken to 360 degrees.
Meanwhile, in a shallow dish mix the flour, salt, and pepper and set aside. Remove the chicken from the brine and let the excess liquid fall off. Dredge the chicken in the flour mixture, then back in the buttermilk, and then back in the flour again.
Place the breaded chicken in the oil and let it fry for a 10 minutes until the center is cooked through and the crust is crunchy, flipping the chicken if necessary. Remove from heat and place on a paper towel. Sprinkle with a little bit of salt.
Turn your broiler on and build your sandwiches. Smear mustard on the inside of the bun; place ham on one side and cheese on the other. Place all the halves under the broiler until the cheese has melted and the ham has begun to crisp up. Remove from heat, put the fried chicken breast in the middle and close. Serve immediately.
Glass Bakeware Warning
Do not use glass bakeware when broiling or when a recipe calls to add liquid to a hot pan, as glass may explode. Even if it states oven-safe or heat resistant, tempered glass products can, and do, break occasionally.