Make the remoulade sauce: mix all the ingredients together in a bowl and set aside for 30 minutes or, even better, overnight.
Heat oil in pan: Pour enough peanut oil in a large frying pan to come up about ½ inch, and set the pan over medium-high heat until a small amount of flour sizzles immediately when you drop some in.
Dredge shrimp: Mix the cornmeal, flour, Cajun seasoning and salt in a large bowl. Working with a few at a time, dredge the shrimp in the egg, then in the cornmeal-flour mixture.
Fry shrimp: Shake off any excess breading and fry the shrimp until golden on both sides, about 2 minutes total. Set the fried shrimp on rack set over paper towels to drain.
Assemble sandwiches: To assemble the sandwiches, slice the sandwich loaves almost all the way through and smear remoulade on both the top and bottom. Lay down a layer of shredded lettuce on the bottom of the sandwich, then arrange the shrimp on top. Lay 3-4 slices of tomato on the shrimp and press the top of the bread down on the bottom, compressing the sandwich a little.