Chick-fil-a copycat chicken sandwiches

1. Cut the chicken breast in half horizontally, to make 4 thin pieces. Place each piece between heavy plastic, and pound to 1/8 thick with a mallet of skillet. Season the chicken with 1 teaspoon kosher salt, 1/2 teaspoon pepper, and 1/2 teaspoon paprika.
In a shallow baking dish, whisk together egg, milk, and 2 tablespoons water. In another baking dish, whisk together both types of flour, dry milk, powdered sugar, baking soda, dry mustard, and remaining 1/2 teaspoon paprika, and 1 teaspoon each salt and pepper. Meanwhile, heat about two inches of peanut oil to 325 degrees in a heavy-bottomed pot or cast iron skillet. While oil heats, slice pickle, and set aside.
Working in batches, dip chicken in the egg mixture, turning to coat, then dredge in flour mixture and shake off any excess. Fry the chicken in hot oil, using a candy thermometer to monitor oil temperature, until golden brown, about 4 minutes. Drain on paper towels.
Heat a large skillet over medium heat. Spread the cut side of the buns with some butter, and lightly toast in the skillet, buttered-side down. To assemble sandwiches, spread grilled buns with more butter, dip 2 pickle slices in jarred pickle juice to moisten and place on the bottom bun. Top with a piece of fried chicken and the bun top.