Gather all ingredients. Place chicken pieces in a large bowl.

Whisk buttermilk, pickle brine, hot sauce, and egg together in a bowl; pour over chicken and stir to ensure each piece is thoroughly coated. Cover and marinate chicken in the refrigerator 2 to 4 hours.

Combine flour and fine salt in a shallow flat dish. Remove chicken from marinade; blot with paper towels. Reserve marinade. Toss chicken in flour until thoroughly coated. Return chicken to marinade, coating all sides; remove chicken from marinade allowing excess to drip back into the bowl. Toss chicken again in flour mixture; place on a rack. Set aside at room temperature to allow coating to dry out a bit, about 15 minutes.

Place butter and lard in a large pot; add cayenne pepper, brown sugar, paprika, garlic powder, kosher salt, and black pepper. Place over medium-high heat; cook and stir until fats melt. Remove from heat; keep sauce warm.

Fill a cast-iron skillet about ⅓ of the way with vegetable oil. Heat oil to 350 degrees F (175 degrees C) over medium-high heat. Carefully place chicken into hot oil, skin-sides down. Maintain an oil temperature of 325 degrees F (165 degrees C), adjusting heat as needed. Fry until an instant read thermometer inserted into thickest parts, near but not touching bones, reads 165 degrees F (74 degrees C), 8 to 10 minutes per side.

Transfer chicken to a rack to drain. Brush both sides with sauce, stirring the sauce first if separation occurs—this is normal due to the melted fats.