Pound each cutlet to an even 1/2-inch thickness and refrigerate it in the pickle brine for 1 hour.
Heat the peanut oil in a deep skillet to 350°F, then whisk the milk and egg in one bowl and the flour, sugar, paprika and salt in another.
Drain the chicken, dip each piece in the milk mixture, and press it firmly into the seasoned flour until craggy bits cling.
Fry the cutlets one at a time for 4 to 6 minutes, turning once, until deeply golden and 165°F in the center.
Drain the chicken on a rack for 3 minutes, then set each cutlet on a bun with 3 pickle chips.
