Whisk the buttermilk, pickle brine, hot sauce, and egg in a large mixing bowl. Add the chicken, and toss to coat. Cover with plastic wrap and refrigerate for 2 to 4 hours.
Just before frying, mix the flour and salt in a shallow flat dish. Set aside.
Remove the chicken pieces from the marinade and blot gently with paper towels. Don’t discard the marinade. Toss the chicken pieces in the flour mixture until evenly coated. Return the chicken to the marinade and thoroughly coat all sides. Let the excess drip back into the bowl. Coat the chicken in the flour mixture again, then place them on a rack to dry slightly – about 15 minutes.
While the chicken dries, make the sauce. Add the butter, lard, cayenne pepper, brown sugar, paprika, garlic powder, kosher salt, and black pepper to a large pot over medium-high heat. Stir until melted and smooth, then remove from the heat or leave on low, stirring occasionally.
Pour the vegetable oil into a cast iron skillet until 1/3 of the way full. Heat the oil to 350 degrees Fahrenheit (175°C).
Gently place the chicken pieces into the hot oil, skin side down. Fry in batches to maintain an oil temperature of at least 325 degrees Fahrenheit (160°).
Fry the chicken pieces until the internal temperature reads 160 degrees Fahrenheit (70°) – about 8 to 10 minutes per side. Check the internal temperature using an instant-read thermometer.
Move the crispy chicken to a rack to drain. After about 5 minutes, brush both sides of the chicken with sauce before serving. Enjoy!