Sprinkle the chicken breast with salt and pepper and set aside. Mix the flour and cayenne in a shallow dish or bowl. Stir together the egg, buttermilk and 1 tablespoon hot sauce in a second shallow dish or bowl. Add the breadcrumbs to a third shallow dish. Coat each chicken breast by dredging in the flour mix, then dipping in the egg/buttermilk mixture and then finally in the breadcrumbs. Set aside.
To a bowl, add the remaining cup of Louisiana hot sauce and 2 tablespoons of the melted butter. Mix together and set aside.
Heat the olive oil and remaining 4 tablespoons butter in a large skillet over a medium heat. When the oil is hot and the butter has melted, add the chicken pieces to the skillet and fry until golden and cooked through, about 4 minutes per side. Remove and set aside. One by one dip the crisp chicken into the Louisiana hot sauce and butter mixture, turning to coat completely.