Make the remoulade: Mix the mustard, ketchup, Worcestershire sauce, garlic, lemon juice, paprika, white pepper, cayenne and sugar in a large bowl; season with salt. Whisk in the olive oil in a slow stream until blended. Whisk in the celery, parsley, onion, scallion, mayonnaise and hot sauce. Cover and refrigerate until ready to serve.
Prepare the shrimp: Bring 2 quarts water to a boil in a large pot. Add 3 tablespoons salt, the lemon slices, hot sauce, bay leaves, carrot and Worcestershire sauce; boil 10 to 15 minutes. Add the shrimp and return to a boil, then reduce the heat and simmer until the shrimp are opaque and just firm, 5 to 7 minutes. Drain the shrimp and run under cold water to stop the cooking. Discard the carrot, lemon slices and bay leaves. Cover the shrimp and refrigerate until cold.
Fry the tomatoes: Mix the cornmeal, 1/4 teaspoon salt and teaspoon black pepper in a shallow dish. Put the buttermilk in another shallow dish. Heat the vegetable oil in a large deep skillet over medium-high heat. Dip the tomato slices in the buttermilk, then coat with the cornmeal, shaking off the excess. Fry until golden brown, 1 to 2 minutes per side.
Place 2 fried tomato slices on each plate. Top with the shrimp and drizzle with the remoulade.