01 - Whisk together buttermilk, Cajun seasoning, smoked paprika, garlic powder, onion powder, cayenne pepper, salt, and pepper in a bowl. Add chicken breasts, cover, and refrigerate for at least 30 minutes, up to 4 hours for enhanced flavor.
02 - Combine mayonnaise, minced garlic, lemon juice, Dijon mustard, salt, and black pepper in a small bowl. Mix thoroughly until smooth. Refrigerate until ready to serve.
03 - Mix flour and cornstarch in a shallow dish. Remove chicken from marinade, allowing excess to drip off. Press each breast into flour mixture, coating evenly and lightly pressing to adhere the breading.
04 - Heat 1 inch of vegetable oil in a large skillet or Dutch oven to 350°F. Fry chicken breasts for 5-7 minutes per side until golden brown and internal temperature reaches 165°F. Drain on wire rack or paper towels.
05 - Spread garlic aioli on both halves of toasted buns. Layer lettuce on bottom bun, add fried chicken breast, tomato slice, and pickles. Close with top bun and serve immediately.