Boil the Water: In a large pot, bring 4 cups of water to a boil. Squeeze the juice from the lemon halves into the water, then drop the lemon halves into the pot. Add the Old Bay seasoning, bay leaves, and salt to the water.
Cook the Shrimp: Add the shrimp to the boiling water and cook for 2-3 minutes, or until the shrimp turn pink and opaque. Be careful not to overcook the shrimp, as they can become tough.
Cool the Shrimp: Using a slotted spoon, transfer the cooked shrimp to an ice bath. Let them cool completely for about 5 minutes. This step helps stop the cooking process and keeps the shrimp tender.
Drain and Chill: Once cooled, drain the shrimp and pat them dry with paper towels. Place the shrimp in the refrigerator for at least 30 minutes to chill.
Combine Ingredients: In a mixing bowl, whisk together the ketchup, horseradish, lemon juice, Worcestershire sauce, and hot sauce (if using).
Season: Taste the sauce and adjust the seasoning with salt and pepper. If you prefer a spicier sauce, add more horseradish or hot sauce.
Chill the Sauce: Cover the sauce and refrigerate it until ready to serve.
Arrange the Shrimp: On a serving platter or individual cocktail glasses, arrange the chilled shrimp in a circular pattern.
Add the Sauce: Place a small bowl of cocktail sauce in the center of the platter or add a dollop of sauce to each glass.
Garnish and Serve: Garnish with lemon wedges or parsley, if desired, and serve immediately.