Season the chicken liberally with salt and black pepper on both sides and set aside.
In a shallow dish, whisk together the flour, cornstarch, baking powder and a pinch of salt. In a separate shallow dish, whisk together the buttermilk, egg and hot sauce. Dredge the chicken by first coating it in flour, then dipping it into the buttermilk, and finally returning to the flour mixture, making sure to pat down firmly on both sides. Shake off excess flour and transfer to a baking sheet. Continue dredging until all the chicken is coated. Allow to rest while you heat up the oil.
Add a scant ½ inch of peanut oil to a cast-iron skillet and set over medium-high heat. Bring the oil up to 360°F. Once hot, carefully add about two pieces of chicken at a time. Fry until golden brown, about 4 1/2 minutes per side. Transfer to a wire rack set over a baking sheet and sprinkle with salt. Continue frying the remaining two. You can keep the chicken warm in a 250°F oven.
While the chicken fries, combine the cayenne, brown sugar, garlic powder, paprika, and black pepper in a heatproof bowl. Once all the chicken is done, carefully add about 1/2 cup of the hot frying oil to the bowl with the spices and whisk until smooth. Dunk the fried chicken in the spiced oil. (If it gets too thick at any point, just thin out with a little more hot oil.)
To build the sandwiches, toss the lettuce with a spoonful of the mayo. Slather the bottom buns with mayo, top with the lettuce, a piece of chicken and then with pickles. Slather the top buns with more mayo, and then close the sandwiches. Serve immediately and enjoy!