Mix mayonnaise, Creole mustard, and pickle brine; refrigerate while cooking shrimp.
Soak shrimp in buttermilk 10 minutes.
Whisk flour, cornmeal, Cajun seasoning, and salt in a shallow dish. Lift shrimp from buttermilk; press into dredge.
Heat oil in a heavy pot to 350°F; keep pot no more than half full.
Fry shrimp in three uncrowded batches 2 to 3 minutes, maintaining 340°F to 350°F, until crisp and centers reach 145°F.
Drain batches unstacked on a rack over a sheet.
Split rolls; spread both sides with remoulade. Fill each with lettuce, 2 tomato slices, 4 pickles, and one-quarter shrimp.
Close firmly; serve while shrimp and crust remain crisp.