Butterfly each chicken breast into two thinner cutlets (about 1/2 inch thick). Pat dry.
Whisk together 3/4 cup pickle juice and 1/4 cup buttermilk. Submerge the chicken and refrigerate 30 minutes (or up to overnight for deeper flavor).
In a shallow bowl, combine flour, cornstarch, salt, pepper, paprika, garlic powder, and cayenne. In a second bowl, beat the egg with 3 tablespoons buttermilk until smooth.
Preheat the air fryer to 390°F for 5 minutes. Lightly mist the basket with oil spray.
Drain chicken well and blot excess brine. Dredge each cutlet in the flour mixture, dip in the egg mixture, then return to the flour. For extra craggy bits, flick a teaspoon of leftover brine into the flour and toss to create little clumps before pressing it onto the chicken.
Set breaded chicken on a rack for 10 minutes to hydrate the coating. While it rests, warm the split biscuits in a 300°F air fryer or 325°F oven for 2–3 minutes.
Mist both sides of the chicken generously with oil spray and arrange in a single layer in the hot basket. Air fry for 7 minutes, flip, spray again, and cook 5–7 minutes more, until golden and the thickest part reaches 165°F.
Rest the chicken 2 minutes. Tuck each cutlet into a warm biscuit and serve immediately.