Pour the pickle juice into a large ziplock bag. Add the chicken pieces and let them sit in the brine in the refrigerator for at least 2 hours, or up to overnight.

Set out two shallow dishes. In the first, mix together the flour, cornstarch, and Creole seasoning. In the second, pour the buttermilk and hot sauce.

Dunk each chicken piece into the flour mixture, then the buttermilk mixture, then back in the flour mixture. Place the breaded pieces on a wire rack set on a baking sheet.

Pour the oil into a large pot—it should come about a third to halfway up the pot sides—and heat over high heat until the oil reaches 350°F. (To check the temperature, use a cooking thermometer dipped into the oil or clipped to the side of the pot.)

Use tongs to carefully place half the chicken pieces in the oil. Fry for 7 to 10 minutes, depending on the size of the pieces (small thighs will cook faster than large breasts). Repeat with the remaining chicken pieces, then turn off the heat.

To make the spicy oil for the chicken, transfer at least a cup of the used cooking oil into a heatproof bowl. Add the cayenne pepper, paprika, brown sugar, chili powder, garlic powder, and salt, then mix everything together. Use a brush to coat the cooked chicken pieces with the spicy oil.