Pat the chicken breasts dry and place them in a single layer in a 13×9-inch baking dish. Evenly sprinkle 1 1/2 tablespoons coarse salt and 1 teaspoon ground pepper over all sides, cover, and refrigerate for 4 to 24 hours to dry brine.
Whisk together the seasoned flour: combine 1 1/2 cups all-purpose flour, 1 1/2 cups cornstarch, 2 tablespoons baking powder, 1 tablespoon paprika, 4 teaspoons coarse salt, and 1/2 teaspoon ground pepper in a wide shallow bowl. Set aside.
In a separate bowl, whisk 5 large eggs with 1/2 cup buttermilk and a pinch of salt and pepper to make the egg wash. Set aside.
Heat oil in a 4–5 quart heavy pot or Dutch oven to 350°F. Fill the pot to about halfway with oil. Maintain temperature; adding cold chicken will drop it to roughly 325°F.
Working one breast at a time, press each chicken piece into the seasoned flour to coat, shake off excess, dip fully into the egg wash, then return to the flour and press again to form a thorough breading. Place breaded breasts on a wire rack set over a sheet tray and rest up to 15 minutes; repeat until all pieces are breaded.
Fry the chicken in batches (2–3 pieces at a time) at 325–350°F for about 10–12 minutes per breast, until golden brown and cooked through (internal temperature around 165°F). Transfer to a wire rack set over a sheet tray and keep warm in a 200–225°F oven while finishing remaining batches.
Make the hot sauce while the chicken cooks: in a small saucepan combine 3/4 cup hot fryer oil, 3 tablespoons cayenne, 3 tablespoons honey, 1 teaspoon chili powder, 2 teaspoons garlic powder, 2 teaspoons onion powder, and 2 teaspoons coarse salt. Warm over low–medium heat, stirring occasionally, until honey is dissolved and the mixture is blended.
Brush or spoon the hot sauce onto both sides of each cooked chicken breast while the sauce and chicken are hot so the sauce adheres.
To assemble sandwiches, spread mayonnaise on the bottom toasted bun, add a sauced chicken breast, top with coleslaw (if using) and pickles, then finish with the toasted top bun.