Step 1

For the shrimp: Fill a large pot with 8 cups cold water. Squeeze in the lemon juice, then add the lemon halves. Add the onion, garlic, Old Bay, bay leaf, salt and peppercorns and bring to a simmer over medium heat; cook for 20 minutes. Scoop out the solids and return the liquid to a simmer.

Step 2

Fill a large bowl halfway with ice. Add 3 cups of water and place a smaller bowl inside (but don’t let the water get in the smaller bowl!).

Step 3

Add the shrimp to the pot with the simmering liquid and stir, then cover and turn off the heat. Let sit until the shrimp are pink, curled and opaque throughout, 3 minutes for smaller shrimp and 4 minutes for larger shrimp. Using a slotted spoon, transfer the shrimp to the bowl set over the ice bath. Gently stir every few minutes to cool down the shrimp. Once they’re no longer steaming, put the shrimp on a platter and refrigerate until cold, at least 30 minutes.

Step 4

Meanwhile, for the cocktail sauce: Stir the ketchup, horseradish, hot sauce, Worcestershire sauce, salt and pepper in a small bowl. Chill at least 30 minutes before serving. Serve with the shrimp.