In a small bowl, whisk together the mayonnaise, ketchup, parsley, scallion, cornichons, capers, paprika, Dijon mustard and cayenne until thoroughly combined.
Taste the sauce and season to taste with salt and pepper, as needed. Cover and refrigerate until ready to use. Can be made up to a week in advance.
For the shrimp:
Add the buttermilk to one medium mixing bowl and add the shrimp. In another medium mixing bowl whisk together the cornmeal, flour, paprika, cayenne, garlic powder and pepper.
Fill a large cast iron pan or dutch oven with enough vegetable oil to reach 1” up the side. Heat the oil to 350ºF (180ºC).
Working a few shrimp at a time, toss the shrimp in the cornstarch mixture and toss to coat then add to the oil and fry until golden brown on both sides, about 3 minutes total. Remove to a paper towel-lined plate to drain. Continue with the remaining shrimp.
For serving:
Use your fingers to scoop out some of the inside of the bottom half of the rolls and discard or save for breadcrumbs.
Fill each roll with the fried shrimp then top with shredded iceberg lettuce, tomato, pickles and remoulade. Close the sandwich and cut in half. Serve with hot sauce on the side.