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Pour oil to a depth of 2 inches in a large deep skillet; heat over medium-high to 370°F. While oil heats, whisk together eggs, milk, and hot sauce in a shallow dish; add shrimp to the mixture, and toss to coat. Whisk together flour, cornmeal, salt, black pepper, and cayenne pepper in a separate shallow dish.
Serve fried shrimp with lemon wedges, cocktail sauce, and rémoulade if desired.
Prep Time: 15 minutes | Cooking Time: 30 minutes | Total Time: 45 minutes | Servings: 6