Marinate the boneless, skinless chicken breasts in buttermilk and Cajun seasoning for at least 30 minutes in the refrigerator.

Create a dredging station by combining all-purpose flour and cornstarch in a shallow dish, seasoning with additional Cajun seasoning if desired.

Heat enough vegetable oil in a cast-iron skillet to cover the bottom with about 1/2 inch of oil, reaching approximately 350°F.

Dredge the marinated chicken breasts in the flour mixture and fry for about 5-7 minutes on each side until golden brown and cooked through.

Prepare the garlic aioli by mixing mayonnaise, minced garlic, lemon juice, and salt in a bowl until well combined.

Assemble the sandwich with a layer of aioli on the bottom half of the bun, followed by lettuce, fried chicken, and the top bun.

Serve the sandwich immediately while hot, optionally with side fries or salad.