Make Remoulade: Mix all remoulade ingredients in a bowl, set aside for at least 30 minutes.
Heat Oil: In a large frying pan, heat peanut oil to medium-high, enough to come up 1/4 inch.
Dredge Shrimp: Mix cornmeal, flour, Cajun seasoning, and salt in a bowl. Dip shrimp in beaten eggs, then coat in the mixture.
Fry Shrimp: Fry shrimp for 2 minutes on each side until golden. Remove and drain on paper towels.
Assemble Sandwiches: Spread remoulade on sandwich rolls, layer with shredded lettuce, fried shrimp, and tomato slices.
Serve: Press the sandwich together and serve immediately, with hot sauce and a cold beer.