In a large pot, combine 6 cups water, 1 tablespoon kosher salt, 1 bay leaf, and 1 teaspoon whole black peppercorns. Cut the lemon in half and add both halves (juice and rinds) to the pot. Bring the liquid to a rolling boil over high heat.

Cook shrimp

Once the poaching liquid is boiling, add the shrimp all at once. Return to a gentle boil and cook until the shrimp are opaque and just firm, about 2 to 3 minutes for large (16/20) shrimp. Do not overcook.

Shock shrimp

While shrimp cook, prepare a bowl with 2 cups ice and 1 cup cold water to make an ice bath. Immediately transfer the cooked shrimp from the pot into the ice bath using a slotted spoon to stop cooking. Let them sit in the ice bath for 3 to 4 minutes until completely chilled.

Peel and chill (optional)

If shrimp are not already peeled, remove shells leaving tails intact (for presentation). Pat shrimp dry with paper towels and keep chilled in the refrigerator until ready to serve.

Cocktail sauce

Mix sauce

In a medium bowl, combine 1 cup chilled ketchup, 3 teaspoons prepared horseradish (start with 2 tsp and adjust), 2 tablespoons fresh lemon juice, 1 teaspoon Worcestershire sauce, 1 teaspoon hot sauce, 1 teaspoon smoked paprika, 1 teaspoon sea salt, and 1/2 teaspoon freshly ground black pepper. Whisk until smooth and taste; adjust horseradish, hot sauce, or lemon to balance heat and acidity.

Chill sauce

Cover the sauce and refrigerate for at least 15 minutes to let flavors meld. For best flavor, make the sauce 30–60 minutes ahead.

Garnish / Serving

Arrange chilled shrimp on a platter over a bed of ice or on chilled serving plates. Place the cocktail sauce in a small bowl in the center or individual ramekins for dipping. Garnish with lemon wedges and chopped fresh parsley. Serve immediately.