In a large bowl, whisk together buttermilk, hot sauce, and salt. Add chicken pieces, turn to coat, cover, and refrigerate for at least 30 minutes (or up to overnight for deeper flavor).

In a second bowl, whisk flour, cayenne, paprika, garlic powder, onion powder, salt, and pepper. Set a wire rack over a baking sheet next to the dredge station.

Pour oil (or lard) into a large heavy-bottomed pot or deep fryer to a depth of 3 inches. Heat over medium-high until a deep-fry thermometer reads 350°F (175°C).

Lift each chicken piece from the buttermilk, letting excess drip off. Dredge thoroughly in the flour mixture, pressing firmly to adhere. For an extra-crunchy crust, dip back into buttermilk and dredge a second time. Place on the wire rack.

Carefully lower chicken into the hot oil, skin-side down, in batches to avoid crowding. Fry for 12–15 minutes, turning once, until deep golden brown and an instant-read thermometer inserted into the thickest part registers 165°F (74°C). Drain on a clean wire rack.

While the last batch fries, ladle 1/2 cup of the hot frying oil into a heatproof bowl. Whisk in cayenne, brown sugar, paprika, garlic powder, and salt until smooth. The mixture will bubble—that's normal.

As soon as each batch comes out of the oil, use a pastry brush or spoon to generously coat the chicken all over with the hot paste. Place each coated piece directly onto a slice of white bread, pile on pickle chips, and drizzle any remaining paste over the top.