Place your chicken breasts between two sheets of plastic wrap and pound them to an even half-inch thickness. This helps the chicken cook through quickly and evenly instead of drying out on the edges. Slice each piece a bit larger than your bun so it doesn't shrink too small once fried.
Whisk together the buttermilk, egg, and salt in a large bowl, then set aside two tablespoons of that mixture for later. Add the chicken, coat it well, cover, and refrigerate for at least an hour, or up to a full day. The longer soak really does make the chicken more tender.
In a separate bowl, whisk the flour, cornstarch, and all the seasonings together. Then add the reserved two tablespoons of marinade right into the dry mix and rub it in with your fingers. This creates little craggy clumps that fry up extra crunchy instead of smooth and flat.
Pour the oil into a large, heavy pot and heat it over medium-high heat to 350°F, using a thermometer if you have one. Keeping the temperature steady is the difference between crispy chicken and greasy chicken, so try not to let it swing too high or too low.
Lift the marinated chicken with tongs, letting the excess drip off, then press it firmly into the breading on both sides. Shake off any loose bits, then lower it carefully into the hot oil. Fry for about two minutes per side, flipping once, until deeply golden and cooked through.
Move the fried chicken to a wire rack right away so it doesn't sit in its own grease. If you're adding cheese, place it on top now so it melts from the residual heat. While that happens, butter your buns and toast them in a dry skillet until golden brown.
Spread your sauce generously on both halves of the toasted bun. Layer on lettuce, tomato, the crispy chicken, and pickles if you're using them. Close up the sandwich and serve it immediately while everything is still warm and crunchy.