Place each chicken breast between two sheets of heavy plastic on a solid, level surface. Firmly pound chicken with the smooth side of a meat mallet to an even thickness. Cut each breast in half and place in a bowl. Pour pickle brine on top and let sit for 1 hour.

Meanwhile, mix flour, powdered sugar, salt, paprika, pepper, celery salt, and basil in a bowl.

Whisk eggs and milk together in another bowl.

Drain liquid from the chicken and rinse off briefly. Shake any excess liquid from chicken.

Heat oil in a deep-fryer or large skillet to 350 degrees F (175 degrees C).

Dip each piece of chicken into the flour mixture, then into the egg-milk mixture, then coat again with the flour. Dip each piece again, if desired.

Deep-fry chicken, a few pieces at a time, until golden brown, 2 to 3 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).

Let chicken rest on a cooling rack set over a baking sheet for 5 minutes. While chicken is resting, lightly butter each sandwich bun and toast them in a skillet.

Add 2 pickle slices to the bottom of each bun, then a chicken piece, then top with the other bun. Repeat to make remaining sandwiches.