In a medium saucepan, combine 6 cups water, 1 tablespoon kosher salt, 6 peppercorns, and 1 bay leaf. Cut the lemon in half and squeeze both halves into the pot, then drop the halves in as well. Bring the liquid to a gentle boil over medium-high heat.

Cook shrimp

As soon as the liquid reaches a rolling boil, add the 8 prepared large shrimp. Return to a gentle boil and cook until shrimp are opaque, pink, and firm, about 2 to 3 minutes depending on size. Do not overcook.

Shock shrimp

While the shrimp cook, fill a large bowl with the 3 cups of ice and additional cold water if needed to create an ice bath. Using a slotted spoon, transfer cooked shrimp immediately to the ice bath to stop cooking. Chill for 3 to 5 minutes until completely cool.

Dry and chill

Remove shrimp from the ice bath and pat dry with paper towels. Refrigerate on a plate, covered, until ready to serve (can be held up to 2 hours). Reserve poaching liquid or discard.

Cocktail sauce

In a small bowl, combine 1 tablespoon ketchup, 1 teaspoon prepared horseradish, 1/2 tablespoon fresh lemon juice, 1/4 teaspoon Worcestershire sauce, and 1 teaspoon hot sauce if using. Season with 1/8 teaspoon salt and a pinch (1/16 tsp) black pepper. Stir until smooth and taste; adjust horseradish or hot sauce for desired heat.

Cover and refrigerate the sauce for at least 10 minutes to let flavors meld. Sauce can be made up to 24 hours ahead.

To serve

Arrange 8 chilled shrimp around a small serving bowl or glass containing the cocktail sauce. Garnish with lemon wedges and a sprinkle of chopped parsley if desired. Serve immediately.