In a large bowl, stir together the egg, shrimp, butter, salt, pepper and cayenne.
Add the flour and stir until blended.
Fill a large pot with oil about 2" high and heat to 375 degrees.
Drop about 1 tablespoon of batter into the oil and fry until golden brown. It only takes a few minutes.
Drain shrimp on some paper towels.
Serve immediately.