Halve chicken breasts crosswise so you have 8 cutlets. Place each cutlet between two pieces of plastic wrap and gently pound thicker areas to uniform thickness. Season cutlets on both sides with salt and pepper.
In a large, nonreactive bowl combine buttermilk, mustard, about 1/2 teaspoon salt, a pinch of black pepper,and several dashes of hot sauce; mix well. Place chicken cutlets in buttermilk mixture, stirring to coat each piece. Place in refrigerator and marinate 10 minutes.
Meanwhile, heat oven to 200 degrees and place a rack on a rimmed baking sheet. Pour enough oil into a 12-inch, heavy-bottomed skillet (preferably cast iron) to measure about 3/4-inch deep and begin heating over medium high.
In a shallow dish, combine flour, 1/2 teaspoon kosher salt and 1/8 teaspoon pepper.
In a separate small bowl, combine honey and 1/2 teaspoon finely ground black pepper; set aside.
When oil reaches 360 degrees, remove 4 chicken cutlets from buttermilk marinade and coat well in seasoned flour mixture. Carefully place cutlets in hot oil and cook, turning once until they are dark golden brown on both sides and just cooked through, about 6 minutes total. Use a slotted spatula to remove finished cutlets to rimmed baking sheet to drain; sprinkle with salt. Keep finished cutlets warm in the oven. Repeat frying process with remaining cutlets. Serve finished cutlets drizzled with black-pepper honey.