Pat shrimp dry with paper towels. Whisk together the egg and milk and add shrimp to mixture. Stur together the flour, Creole seasoning, salt, and peppers in a wide bowl. Dunk the shrimp from the milk mixture in the flour mixture, then move to a work rack set over a plat. Let sit for a moment, then return the shrimp to the flour mixture a second time; shake off excess flour.

Heat oil in a deep skillet over medium-high heat to 375ºF. Fry shrimp in small batches until golden brown, 3-4 minutes per batch. Repeat, returning oil to temperature between batches. Serve hot.