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 fully incorporated.
03 - Pat shrimp dry with paper towels. Dip each shrimp into the egg-buttermilk mixture, allowing excess to drip off, then press firmly into the flour-cornmeal mixture to coat completely. Arrange breaded shrimp on a tray in a single layer.
04 - Pour about 1 inch of vegetable oil into a large skillet or Dutch oven. Heat to 350°F. Fry shrimp in batches for 2-3 minutes per side until golden brown and cooked through. Transfer to paper towels to drain excess oil.
05 - Split French rolls lengthwise, leaving the hinge intact. Lightly toast cut sides under a broiler or in a skillet for enhanced texture and flavor.
06 - Spread remoulade sauce generously on both cut sides of each roll. Layer shredded lettuce, tomato slices, red onion, and pickle chips on the bottom half. Top with a generous portion of fried shrimp. Close sandwiches and serve immediately.