In a zip-top bag combine pickle juice and water. Add chicken breast halves and refrigerate at least 30 minutes and up to overnight. Pat dry before breading.

In a bowl, whisk the mayonnaise, Dijon, yellow mustard, barbecue sauce, honey, garlic powder, paprika, and lemon juice. Taste and adjust honey or mustard. Chill while you cook.

In a large bowl mix flour, powdered sugar, paprika, black pepper, chili powder, salt, baking powder, and cayenne (if using). In another bowl whisk milk and egg.

Pour 2–3 cups of oil into a deep saucepan or Dutch oven. Heat to 350°F (175°C). Use a candy or frying thermometer for accuracy.

Dip each chicken breast into the milk-and-egg mixture, then dredge in the flour mix. For extra crunch, repeat: back into the egg, then flour again. Press coating into the meat so it adheres.

Carefully lower the breasts into the hot oil, working in batches so you don’t overcrowd the pot. Fry about 3–4 minutes per side until golden brown and an instant-read thermometer reads 165°F in the thickest part. Remove to a wire rack set over a baking sheet to drain.

Lightly butter and toast buns on a skillet or under a broiler. Spread sauce on both bun halves, add the chicken, pickles, and optional lettuce, tomato, or cheese. Serve hot.