In a medium pan, place chicken and cover with milk. Cover with plastic wrap and refrigerate for 2 hours to overnight. This helps tenderize the meat, but is optional
In a large saucepan over a medium-high heat, using tongs, transfer chicken into pot, then pour in the milk. Bring milk to a boil, then reduce heat to medium-low allowing to simmer until the chicken is cooked through entirely, about 20 minutes. Remove the chicken from the milk, and place on a rack to cool. Allow them to sit until warm about 15 minutes, and then pat dry using a kitchen towel.
Heat vegetable shortening in a Dutch oven over high heat just until it's nearly at the smoking point around 325 degrees F.
In a large zip-lock bag, add salt, flour, cayenne pepper, shake to combine.
In a medium bowl, beat 1 egg.
Place each piece of chicken, 1 at a time, in the bag and shake to coat the chicken. Then dip chicken into the egg to coat. Place the chicken back into the flour to coat for a second time. Repeat this method on remaining 3 pieces of chicken.
Gently drop each piece of chicken into hot oil, allowing the skin to crisp and turn golden brown in color, about 1 minute per side. Remove from the oil and transfer to a paper towel-lined plate. Serve immediately.