01 - Combine buttermilk, hot sauce, and Cajun seasoning in a mixing bowl. Add chicken breasts, cover, and refrigerate for at least 30 minutes or up to 4 hours to enhance flavor.
02 - Whisk together all-purpose flour, corn starch, Cajun seasoning, garlic powder, paprika, salt, and black pepper in a separate bowl.
03 - Remove chicken breasts from marinade, allowing excess to drip off. Thoroughly coat each piece in the flour mixture, pressing firmly to ensure adherence.
04 - Heat vegetable oil in a deep skillet or Dutch oven to 350°F. Fry chicken breasts for 6 to 8 minutes per side until golden, crisp, and cooked through to 165°F internal temperature. Transfer to paper towels to drain.
05 - In a small bowl, mix mayonnaise, minced garlic, fresh lemon juice, Dijon mustard, and season with salt and black pepper. Refrigerate until serving.
06 - Toast brioche buns until lightly golden. Spread a generous layer of garlic aioli on both cut sides of each bun.
07 - Layer each bottom bun with lettuce, a fried chicken breast, tomato slices, and pickles if desired. Cap with the top bun and serve immediately.