In a large pot, combine 2 liters of water, 2 tablespoons kosher salt, 1 teaspoon black peppercorns, and 2 bay leaves. Zest the lemon over the pot, then cut it in half and squeeze the juice into the water. Add the squeezed lemon halves to the pot as well. Bring the mixture to a gentle boil over high heat.

Poach the shrimp

Once the liquid reaches a rolling boil, reduce heat so it returns to a gentle simmer. Add the shrimp in a single layer and cook until they are pink, opaque, and just curled — about 2 to 3 minutes for large shrimp. Do not overcook.

Shock and chill

While the shrimp cook, prepare a large bowl with 4 cups of ice and enough cold water to fill. Using a slotted spoon, immediately transfer the cooked shrimp to the ice bath to stop cooking. Let them chill for at least 5 minutes until completely cold. Drain and pat shrimp dry with paper towels. Refrigerate shrimp until ready to serve.

Cocktail Sauce

In a medium bowl combine 1 cup ketchup, 3 tablespoons prepared horseradish, 1 tablespoon fresh lemon juice, 1 teaspoon Worcestershire sauce, 1 teaspoon hot sauce (if using), 1 teaspoon smoked paprika, 1 teaspoon kosher salt and 1/2 teaspoon black pepper. Whisk until smooth. Taste and adjust heat or acidity: add more horseradish for heat, more lemon for brightness, or more ketchup to mellow. Cover and refrigerate for at least 30 minutes to let flavors meld.

Garnish & Assembly

Prepare serving vessel: Fill a shallow platter or individual cocktail glasses with about 4 cups crushed ice (or enough to create a cold bed). Spoon the chilled cocktail sauce into a small bowl or divide into individual ramekins and place on the ice bed.

Arrange shrimp: Neatly arrange the chilled shrimp around the sauce bowl with tails hanging over the edge for easy picking. Sprinkle 2 tablespoons chopped fresh parsley over the shrimp and tuck 6 lemon wedges around the platter. Keep the platter on ice or in the refrigerator until serving.

Serve: Serve immediately, instructing guests to dip shrimp into the cocktail sauce. Leftover shrimp keep refrigerated in an airtight container up to 2 days; sauce keeps up to 5 days refrigerated.