In a large pot, combine the water with the salt, whole peppercorns, Old Bay seasoning, pickling spice, dried dill weed, bay leaf and dried thyme. Stir and then add in the sliced onion and lemon halves.
Bring to a simmer and cook until the flavors blend, about 15 minutes.
Bring the poaching liquid up to a boil and add the shrimp. Cook uncovered until the shrimp turn pink on the outside and the meat is no longer transparent in the center, about 4 to 5 minutes total. Do not overcook as that will make the shrimp tough and chewy.
Drain the shrimp into a colander and then immediately transfer them to a bowl of ice water and stir. This will stop the cooking process and prevent the shrimp from continuing to cook. Keep the shrimp immersed until cold.
Remove the shrimp from the ice water when chilled and then peel and devein them. Cover and put into the refrigerator until service time.
To make the cocktail sauce, whisk together the ketchup, chili sauce, horseradish, lemon juice, Worcestershire sauce, hot sauce and salt in a bowl. Taste and correct any seasonings. Cover and put into the refrigerator until chilled, at least 15 minutes.
To serve, arrange the chilled poached shrimp onto a plate or serving platter, and serve with chilled cocktail sauce garnished with lemon wedges and parsley sprigs if desired.
NOTE: It is a great time saver to make your shrimp cocktail a day or two before and then just chill until it is needed, especially if prepping for a party.