Pat shrimp with paper towels to remove excess moisture. One at a time, dredge shrimp in flour, shaking off excess. Dip into egg wash, allowing excess to drip off.
Heat 2-3 inches of oil in a heavy-bottomed, deep pot to 325 to 350 degrees F. Fry shrimp in batches of 5-6, being sure not to crowd the pot, until the breading is golden and the shrimp are opaque, 3-4 minutes.