Place 2 cups buttermilk in a non-metallic bowl and stir in 1 teaspoon salt and 1 teaspoon black pepper.
Lay each chicken breast on a cutting board and slice horizontally with a sharp knife to create two thinner fillets from each breast.
Cover the fillets with parchment or plastic and pound gently with a meat mallet or heavy pan until the pieces are an even thickness.
Add the chicken fillets to the seasoned buttermilk, cover, and let sit at room temperature for 30–60 minutes to marinate.
In a shallow bowl, combine 1½ cups all-purpose flour, 1 teaspoon ground black pepper, 1 teaspoon salt, 1 teaspoon paprika, ½ teaspoon smoked paprika, ½ teaspoon cayenne (optional), ½ teaspoon onion powder, ½ teaspoon baking soda, and ½ teaspoon baking powder.
Preheat the oven to 230°F (110°C) and set a wire rack or plate in the oven to keep cooked chicken warm.
Remove the fillets from the buttermilk bowl. Whisk 1 egg into the remaining buttermilk to create an egg wash.
Coat each fillet first in the seasoned flour, then dip into the buttermilk-and-egg mixture, and finally dredge again in the flour so each piece is fully coated.
Heat 1 cup vegetable oil in a large heavy-based skillet over medium heat until it reaches about 340°F (170°C) or a small pinch of flour sizzles on contact.
Fry the fillets two at a time. Carefully slide them into the hot oil and cook 2 minutes per side, turning only once, until lightly golden and crisp.
Drain cooked fillets on paper towels, then transfer to the oven to keep warm while you fry the remaining pieces.
Serve the chicken immediately.