Prepare the Shrimp:
Fill a large pot with water, enough to cover the shrimp. Add salt, lemon halves, bay leaves, peppercorns, and garlic to the water. Bring the water to a boil over medium-high heat.
Cook the Shrimp:
Once the water reaches a rolling boil, add the shrimp to the pot. Reduce the heat slightly 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.
Ice Bath:
Prepare a large bowl of ice water. Using a slotted spoon, transfer the cooked shrimp to the ice bath to stop the cooking process and cool them down quickly. Let them sit in the ice bath for a few minutes, then drain and pat dry with paper towels.
Make the Cocktail Sauce:
In a small bowl, combine ketchup, horseradish, lemon juice, Worcestershire sauce, and hot sauce (if using). Stir until well combined. Taste and adjust the seasoning with salt and pepper or more horseradish if you prefer more heat.
Serve:
Arrange the chilled shrimp on a serving platter or individual bowls. Serve with the cocktail sauce on the side for dipping.