2 large eggs, beaten
1 cup whole milk
2 tablespoons chile hot sauce (such as Cholula)
2 pounds large peeled, deveined raw shrimp
3/4 cup (about 3 1/4 oz.) all-purpose flour
2/3 cup (about 2 7/8 oz.) cornmeal
1 1/2 teaspoons kosher salt
1 teaspoon black pepper
1/2 teaspoon cayenne pepper
For serving: lemon wedges, cocktail sauce, rémoulade (optional)
Step 1 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.
Step 2 Remove 6 to 8 shrimp from egg mixture, shaking excess off; dredge in flour mixture. Place dredged shrimp in hot oil; fry until coating is golden and crisp, about 2 minutes. Remove with a slotted spoon to a baking sheet lined with paper towels. Repeat with remaining shrimp, bringing oil back to 370°F over medium-high heat before adding each batch of shrimp.
Step 3 Serve fried shrimp with lemon wedges, cocktail sauce, and rémoulade if desired.