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 together eggs and buttermilk until blended.
03 - Pat shrimp 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. Arrange coated shrimp on a tray.
04 - Pour about 1 inch of vegetable oil into a large skillet or Dutch oven. Heat to 350°F, maintaining temperature throughout frying.
05 - Fry shrimp in batches without overcrowding, 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, leaving one side attached like a hinge. Lightly toast cut sides if desired for added texture.
07 - Spread remoulade sauce generously on both cut sides of each roll. Layer shredded lettuce, sliced tomatoes, red onion, and pickle slices on bottom half. Pile fried shrimp on top and close sandwiches. Serve immediately.