01 - Bring water, lemon slices, salt, and peppercorns to a boil in a medium saucepan over high heat.
02 - Add shrimp to boiling liquid, reduce heat to simmer, and cook until pink and just opaque, about 2-3 minutes.
03 - Remove shrimp with a slotted spoon and immediately transfer to ice water to stop cooking. Drain well and pat dry with paper towels.
04 - Whisk together ketchup, horseradish, lemon juice, Worcestershire sauce, hot sauce if using, and salt in a small bowl until smooth.
05 - Arrange shrimp on serving platter or in cocktail glasses with sauce in a separate dish. Garnish with lemon wedges and parsley. Serve chilled.