Prep the chicken: Split the chicken breasts horizontally to make 4 thin cutlets. Lightly pound to an even 1/2-inch thickness so they cook evenly.
Brine: Add chicken to a bowl or zip-top bag and cover with dill pickle juice.
Chill for 30 minutes to 1 hour. Don’t go longer than 2 hours, or the chicken can get mushy.
Mix the wet dip: In a shallow bowl, whisk milk and egg until smooth.
Mix the dry dredge: In another bowl, combine flour, cornstarch, powdered sugar, salt, pepper, paprika, garlic powder, onion powder, and cayenne (if using).
Heat the oil: Pour 1 to 1 1/2 inches of oil into a heavy skillet or Dutch oven. Heat to 325–340°F. Use a thermometer for best results.
Pat dry and dredge: Remove chicken from brine and pat dry.
Dip in the milk-egg mixture, then coat in the flour mixture. Press the breading onto the chicken so it adheres well. For extra craggy crust, dip back in the wet mixture and dredge again.
Fry in batches: Fry 2 cutlets at a time to avoid crowding.
Cook 3–4 minutes per side, or until golden brown and the internal temperature hits 165°F. Adjust heat to keep the oil in range.
Drain and season: Transfer to a wire rack set over a sheet pan. Sprinkle lightly with salt while hot.
Toast the buns: Melt butter in a skillet over medium heat.
Toast the buns cut-side down until golden and slightly crisp.
Assemble: Place chicken on the bottom bun, add a few dill pickle chips, and cap with the top bun. Serve immediately.