1) In a non-reactive bowl whisk together the buttermilk and the hot sauce. Add the chicken pieces, cover, and refrigerate overnight.
2) In a large brown paper bag combine the flour, paprika, salt, and pepper, and shake to combine. Set a large rack over a baking sheet. Drain the chicken in a colander set in the sink. Put 2 to 3 pieces of the chicken in the bag at a time and shake to coat with the flour. Remove the pieces from the bag and shake off any the excess flour and set on the rack. Repeat with the remaining chicken.
3) Preheat the oven to 125C/Gas 1/2 and line another baking sheet with paper towels. Add enough oil or vegetable fat to two 23cm cast iron skillets so that they are filled 2cm deep. Heat over medium heat until a deep frying thermometer set in the fat registers 190C.
4) Working in batches if needed, add the chicken skin-side down to the skillets, with breasts and wings in one skillet, thighs and legs in the other. Do not crowd the skillets. Fry the chicken until golden brown on one side and turn with tongs to cook the other side. The white meat will take about 20 minutes and the dark about 25 minutes. Drain on the lined pans and keep warm in the oven. Continue until all the chicken is cooked. Serve immediately or at room temperature.