Peel the shrimp, leaving the tails on. With a sharp knife, make a shallow cut down the back of the shrimp and remove the dark veins. Rinse under cold water.
Fill a bowl with ice and water; set aside.
Bring a pot of water to a simmer and add the shrimp. Cook until the shrimp is opaque and floats.
Transfer the cooked shrimp to the ice water to stop the cooking progress. Drain, cover the bowl, and refrigerate the shrimp until serving time.
Combine the remaining ingredients in a bowl; stir to blend thoroughly. Chill thoroughly.
Serve the shrimp ice cold with the cocktail sauce.