01 - Whisk together buttermilk, hot sauce, and Cajun seasoning in a mixing bowl. Submerge chicken breasts in the mixture, cover, and refrigerate for at least 30 minutes, or up to 4 hours for deeper flavor.
02 - In a separate bowl, combine all-purpose flour, corn starch, Cajun seasoning, garlic powder, paprika, salt, and black pepper.
03 - Remove marinated chicken, allowing excess marinade to drip off. Coat each breast in the seasoned flour mixture, pressing firmly to ensure an even, thick crust.
04 - Heat vegetable oil in a deep skillet or Dutch oven to 350°F. Fry the coated chicken breasts for 6 to 8 minutes per side, or until golden, crisp, and the internal temperature reaches 165°F. Drain on paper towels.
05 - Blend mayonnaise, minced garlic, lemon juice, Dijon mustard, salt, and pepper in a small bowl. Refrigerate until ready to use.
06 - Toast split brioche buns until lightly golden. Spread garlic aioli on both cut sides of each bun. Layer lettuce, fried chicken breast, tomato slices, and pickles if desired onto the base of each bun. Cap with the top bun and serve immediately.