Step 1: Pat chicken dry with paper towels. If using breasts, pound to 3/4-inch thickness. In a large bowl, whisk together 2 cups buttermilk, 1 tbsp hot sauce, 1 tsp salt, 1 tsp black pepper, 1 tsp garlic powder, and 1 tsp onion powder. Add chicken, ensuring it’s submerged. Cover and refrigerate for 4-12 hours.
Step 2: For the special sauce, combine 1/2 cup mayonnaise, 2 tbsp ketchup, 1 tbsp yellow mustard, 1 tbsp pickle relish, 1/2 tsp hot sauce, 1/4 tsp garlic powder, and 1/4 tsp paprika in a small bowl. Stir well and refrigerate.
Step 3: In a large, shallow dish, whisk together 3 cups all-purpose flour, 1/2 cup cornstarch, 1 tbsp paprika, 1 tsp cayenne pepper, 1 tsp salt, 1 tsp black pepper, 1 tsp garlic powder, and 1 tsp onion powder for the dry breading mix. In another shallow dish, pour the remaining 1 cup of buttermilk.
Step 4: Remove chicken from brine; do not rinse. Dredge chicken in dry flour mix, pressing firmly. Dip back into buttermilk, letting excess drip. Dip back into dry flour mix, pressing firmly to coat. Place on a wire rack set over a baking sheet. Let rest for 15-20 minutes.
Step 5: Heat 3-4 inches of vegetable oil in a heavy pot to 325°F (160°C). Fry 1-2 chicken pieces for 5-7 minutes per side, until golden brown and internal temperature reaches 165°F (74°C). Remove to a clean wire rack to drain. Repeat with remaining chicken.
Step 6: Increase oil temperature to 350°F (175°C). Return chicken to oil, 1-2 pieces at a time, and fry for another 1-2 minutes per side until exceptionally crispy and darker golden. Remove to wire rack and season lightly with salt.
Step 7: Lightly toast brioche buns. Spread special sauce on both bun halves. Layer lettuce, tomato, red onion (or pickles), and optional cheese on the bottom bun. Place fried chicken, add more special sauce, and top with the other bun. Serve immediately.