Stir together buttermilk and 1 teaspoon cayenne pepper in a large bowl; add chicken, turning to coat. Cover with plastic wrap, and refrigerate at least 6 hours or up to overnight.
In a large brown paper bag, combine flour with remaining 1 teaspoon cayenne, 1 teaspoon salt, and 1 tablespoon pepper; shake to combine. One at a time, place chicken pieces in the bag; shake to coat. Place coated pieces on a clean plate or tray.
In a large skillet, heat 2 inches oil to 350 degrees.using tongs, add chicken one piece at a time, being careful to not overcrowd pan. Fry, turning every 3 to 4 minutes, until deep mahogany in color, about 18 minutes. Remove chicken from skillet, and drain on a brown paper bag. Serve hot, warm, or cold.