Cut chicken breasts and thighs in half. In a large stockpot, combine chicken, 2 quarts cold water, and crab boil. Cover and refrigerate for 8 hours.
In a shallow bowl, combine 1 cup flour, 1 teaspoon salt, and ½ teaspoon pepper. Remove chicken from brine, and pat dry; coat chicken with flour mixture, and place on a rimmed baking sheet in a single layer. Refrigerate for at least 2 hours. (This will help make the fried chicken even crispier.)
In a shallow dish, whisk together Creole seasoning, remaining 2 cups flour, remaining 2 teaspoons salt, and remaining 1 teaspoon pepper. Toss chicken in Creole-seasoned flour mixture, coating liberally and shaking off excess. Place on a wire rack; let stand for 15 minutes.
In a large Dutch oven, pour oil to a depth of 3 inches, and heat over medium heat until a deep-fry thermometer registers 350˚. Fry chicken in batches until a meat thermometer inserted in thickest portion registers 165˚, 9 to 10 minutes. Let drain on paper towels. Season with salt and pepper to taste.
Spread desired amount of mayonnaise onto steamed buns. Top bottom half of buns with lettuce, a chicken breast piece, a chicken thigh piece, and pickles. Cover with top half of buns. Serve with hot sauce, if desired.
