Chef John's Shrimp Cocktail

Stir water onion lemon garlic tarragon seafood seasoning peppercorns and bay leaf together in a large pot; bring to a simmer and cook until flavors blend about 15 minutes.

Whisk ketchup chili sauce horseradish lemon juice Worcestershire sauce hot sauce and salt together in a bowl; refrigerate until chilled at least 15 minutes.

Bring poaching liquid to a rapid boil. Cook the shrimp in the boiling liquid until they are bright pink on the outside and the meat is no longer transparent in the center about 5 minutes. Transfer shrimp to a bowl of ice water and immerse in ice water until cold; drain. Arrange cold shrimp on a platter and serve with chilled sauce.