Stir the mayonnaise, Creole mustard and pickle brine together, then refrigerate the remoulade while the shrimp cooks.
Pour the buttermilk over the shrimp in a bowl and let it stand for 10 minutes.
Whisk the flour, cornmeal, Cajun seasoning and salt in a shallow dish, then lift the shrimp from the buttermilk and press them into the dredge.
Heat the oil in a heavy pot to 350°F, keeping the pot no more than halfway full.
Fry the shrimp in three uncrowded batches for 2 to 3 minutes, maintaining 340°F to 350°F, until crisp and the centers reach 145°F.
Move each batch to a wire rack over a sheet pan and let excess oil drain without stacking the shrimp.
Split the rolls, spread both sides with remoulade and layer each with lettuce, 2 tomato slices, 4 pickle chips and one-quarter of the fried shrimp.
Close each po'boy firmly and serve while the shrimp and crust are still crisp.