Place chicken pieces into a plastic container and cover with buttermilk. Cover and refrigerate for 12 to 24 hours.
Preheat the oil to 170°C.
Drain chicken in a colander. Combine salt, paprika, garlic powder, and cayenne pepper. Liberally season chicken with this mixture. Dredge chicken in flour and shake off excess.
Place chicken skin side down into the pan. Put thighs in the center, and breast and legs around the edge of the pan. Cook chicken until golden brown on each side, approximately 10 to 12 minutes per side. More importantly, the internal temperature should be right around 180 degrees. (Be careful to monitor shortening temperature every few minutes.)
Drain chicken on a rack over a sheet pan. Don't drain by setting chicken directly on paper towels or brown paper bags. If you need to hold the chicken before serving, cover loosely with foil but avoid holding in a warm oven, especially if it's a gas oven.