Using a deep fryer, add oil to maximum fill line in bowl. Select 350ºF and preheat oil. While oil is preheating, rinse, peel and devein shrimp, leaving the tails on. Drain.
Place eggs in a shallow dish and beat well. In a second shallow dish, combine flour, salt, pepper and cayenne pepper. In a third dish, place panko.
Dredge each shrimp in flour, then egg and then panko, coating each piece thoroughly. Transfer shrimp to a large plate.
Place 6 pieces of shrimp in the deep fryer basket and carefully lower it into the preheated oil.
Cook about 2 1/2 - 3 minutes, until golden brown. Carefully lift basket out of oil and lock it onto resting hooks. Allow shrimp to drain and then remove and transfer to a wire rack with a pan underneath.
Repeat the process with remaining shrimp. Serve shrimp with lemon wedges.