01 - Whisk together mayonnaise, Dijon mustard, horseradish, ketchup, lemon juice, parsley, capers, celery, hot sauce, smoked paprika, and minced garlic in a bowl until smooth. Season with salt and pepper to taste. Cover and refrigerate until ready to use.
02 - In one shallow dish, combine flour, cornmeal, Cajun seasoning, paprika, garlic powder, salt, and black pepper. In a second dish, whisk eggs and buttermilk together until blended.
03 - Pat shrimp completely dry with paper towels. Dip each shrimp into the egg-buttermilk mixture, allowing excess to drip off. Dredge in the flour-cornmeal mixture, pressing lightly to adhere coating evenly. Place breaded shrimp on a tray.
04 - Pour 1 inch of vegetable oil into a large skillet or Dutch oven. Heat to 350°F over medium-high heat. Maintain temperature throughout frying for optimal crispiness.
05 - Fry shrimp in batches without overcrowding the pan, 2 to 3 minutes per side, until golden brown and cooked through. Transfer to paper towels to drain excess oil.
06 - Split French rolls lengthwise, keeping one side attached as a hinge. Lightly toast cut sides under a broiler or in a skillet for added texture.
07 - Spread remoulade sauce generously on both cut sides of each roll. Layer shredded lettuce, sliced tomatoes, red onion, and pickles on bottom half. Pile fried shrimp on top. Close sandwiches and serve immediately.