Place each chicken breast between two pieces of plastic wrap and pound with a meat mallet until about 1/2-inch thick; then halve each breast to make 4 cutlets if not already halved.
In a zip-top bag combine 1/2 cup buttermilk and the 1/2 cup dill pickle juice, add the chicken, seal, and refrigerate to marinate for at least 30 minutes; drain well before proceeding.
In a shallow dish whisk the remaining 1 cup buttermilk with the large egg until smooth.
In a clean zip-top bag combine the flour, powdered sugar, kosher salt, paprika, black pepper, onion powder, and garlic powder; seal and shake to mix.
Working one piece at a time, place chicken in the flour bag and shake to coat completely, then dredge in the egg-buttermilk mixture, and return to the flour bag to coat again; shake off excess and rest on a metal cooling rack.
For frying: heat 1 cup peanut oil in a large skillet over medium-high until shimmering, then working in batches cook the chicken 5–6 minutes per side until golden and cooked through to 165°F; drain on paper towels.
For air-frying: preheat the air fryer to 350°F and lightly oil the basket; place chicken in a single layer (work in batches), lightly spray or brush with oil and air fry 6 minutes, flip, spray again and air fry 6 minutes more; increase temperature to 400°F and continue 8 minutes, or until crispy and 165°F internal.
Place each cooked chicken piece on a bun, add Chick Fil A sauce and dill pickle slices, then serve immediately.