01 - Bring 2 cups water, ½ sliced lemon, ½ teaspoon salt, and ½ teaspoon black peppercorns to a boil in a medium saucepan. Add shrimp and reduce heat to a gentle simmer. Cook until shrimp are pink and opaque, approximately 2 to 3 minutes.
02 - Remove shrimp using a slotted spoon and immediately transfer to a bowl of ice water. Allow to cool completely, then drain and pat dry with paper towels.
03 - Combine 3 tablespoons ketchup, 1 tablespoon prepared horseradish, 1 teaspoon fresh lemon juice, ½ teaspoon Worcestershire sauce, ¼ teaspoon hot sauce if desired, and a pinch of salt in a small bowl. Whisk until well blended.
04 - Arrange chilled shrimp on a serving platter or in stemmed cocktail glasses. Place cocktail sauce in a small dish. Garnish with lemon wedges and fresh parsley. Serve immediately.