Heat salt, brown sugar, and 4 cups water in a large pot over medium, whisking, until salt and sugar dissolve, about 5 minutes. Remove from heat and stir in hot sauce and 8 cups ice water. Add chicken to brine, cover, and chill 4 hours.

Combine 2 cups flour and 3 tablespoons Old Bay seasoning in a shallow baking dish and toss with your fingers to evenly distribute seasoning. Place buttermilk in a medium bowl. Remove chicken from brine and pat dry with paper towels.

Working one at a time, dip 8 pieces of chicken in buttermilk, allowing excess to drip off, then coat in flour mixture, packing all around chicken and pressing firmly into cracks and crevices; shake off excess. Place chicken on a wire rack set inside a rimmed baking sheet. Discard flour mixture, which will be wet at this point, and repeat process with remaining flour, Old Bay, buttermilk, and chicken; place on another wire rack set inside a rimmed baking sheet. Chill, uncovered, 12–24 hours.

Let chicken stand at room temperature 30 minutes.

Heat lard, Old Bay, paprika, and cayenne in a small saucepan over low, stirring, until lard is melted, about 3 minutes. Set glaze aside.

Pour oil into a large pot fitted with deep-fry thermometer to come halfway up the sides. Heat over medium-high until thermometer registers 325°. Working in 4 batches, fry chicken, turning often with tongs and adjusting heat to maintain temperature, until skin is deep golden brown and an instant-read thermometer inserted into the thickest part of chicken registers 165° for dark meat and 160° for white meat, 10–12 minutes per batch. Transfer chicken back to wire racks and let rest 5 minutes. Brush lightly with glaze (reheat glaze, if needed) and let cool. Store on racks at room temperature up to 3 hours ahead.