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 maximum flavor penetration.
02 - Combine mayonnaise, minced garlic, lemon juice, Dijon mustard, salt, and black pepper in a small bowl. Mix until thoroughly incorporated and refrigerate until serving.
03 - Mix flour and cornstarch in a shallow dish. Remove chicken from marinade, allowing excess liquid to drip off. Dredge each breast in the flour mixture, pressing lightly to ensure even coating.
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 cooked through, reaching an internal temperature of 165°F. Drain on a wire rack or paper towels.
05 - Spread garlic aioli on both halves of each toasted bun. Layer lettuce on the bottom bun, followed by fried chicken breast, tomato slice, and pickles. Close with the top bun and serve immediately.