In a large bowl, whisk together cider and salt until salt dissolves. Add chicken pieces and enough water to completely submerge and cover the chicken. Let soak 1 hour in the refrigerator. Chicken should be completely submerged in brine.
In a large pot, heat vegetable shortening until a deep-fry thermometer reaches 325 degrees. Line a sheet tray with a wire rack.
In a large bowl, whisk together eggs, cayenne and black pepper. In a paper bag, shake together flour and cornstarch. Drain chicken from brine and dip in batches first in egg mixture then in flour mixture to coat. Set on wire rack to let coating sit for 10 minutes. In 2 batches, fry chicken until golden brown on both sides and cooked through, 15 to 20 minutes, depending on the size of the piece. Remove from oil to drain on paper towel-lined plate.