In a large pot, bring 4 cups of water to a rolling boil over medium-high heat. Add 2 tablespoons of Old Bay seasoning and the juice from the halved lemon, tossing in the lemon halves as well.

Once the broth reaches a vigorous boil, carefully add 1 pound of large shrimp to the pot. Cook for 2 to 3 minutes, stirring occasionally, until they turn bright pink and opaque.

Immediately transfer the cooked shrimp with a slotted spoon into a bowl filled with ice water. Allow to chill for 5 minutes.

In a mixing bowl, combine 1 cup of ketchup, 2 tablespoons of horseradish, and 1 teaspoon of Worcestershire sauce. Add salt and black pepper to taste.

Drain the shrimp and arrange them on a serving platter. Serve with the cocktail sauce and lemon wedges.