To make an easy shrimp cocktail, there has to be a broth to poach the shrimp in and dips. Pre-cooked, frozen shrimp can be used instead of raw for an easier, quicker recipe, but then the cook is unable to control the flavor of the shrimp as precisely.
For the broth, fill a large pot with water, sliced onion, parsley, salt to taste and a halved head of garlic. Carrots, celery, thyme, bay leaves and lemon can also be added for more flavor. Bring this mixture to a boil and add in shelled, deveined raw shrimp. Cook until the shrimp is finished and is a pink color, which takes up to 5 minutes depending on the size of the shrimp. Drain the shrimp from the liquid and discard the other ingredients, then cool the shrimp in the refrigerator or with cool water.
For the sauce, combine ketchup, horseradish, Worcestershire sauce and lemon juice or zest to taste. Hot sauce, salt or other seasonings may be added as desired. Serve both the sauce and shrimp while cold. One popular method of serving this is to hang the curved shrimp around the edges of a bowl with the sauce in the bowl or dish.