In a large saucepan combine 6 cups water, 1 tablespoon kosher salt, bay leaf, peppercorns and the juice of the halved lemon plus the squeezed halves added to the pot. Bring to a rolling simmer over medium-high heat.

Cook shrimp

Add shrimp in a single layer and return to a gentle simmer. Cook until shrimp turn pink and just curl, about 2–3 minutes depending on size. Do not overcook.

Shock shrimp

Immediately transfer shrimp to an ice bath (bowl of ice and cold water) to stop cooking. Let chill for 3–5 minutes until completely cooled. Drain and pat shrimp dry with paper towels. Refrigerate until ready to serve.

Spicy Cocktail Sauce

In a medium bowl combine 3 tablespoons ketchup, 2 tablespoons prepared horseradish, 1 tablespoon fresh lemon juice, 1 teaspoon Worcestershire sauce and 4 dashes hot sauce. Whisk until smooth.

Add 1 teaspoon smoked paprika, 1 teaspoon cayenne pepper, 2 tablespoons finely chopped cilantro and 2 tablespoons finely minced red onion. Stir to combine.

Season with 1 teaspoon sea salt and 1 teaspoon freshly ground black pepper. Taste and adjust heat: add an extra dash or 1/2 teaspoon horseradish for more bite, or more ketchup to mellow. Chill sauce for at least 15 minutes to let flavors meld; can be made up to 24 hours ahead and refrigerated in an airtight container.

Garnish & Serve

Prepare serving bowl: pile crushed ice in a large shallow bowl or individual cups. Arrange chilled shrimp around or on top of the ice with tails outward for easy picking.

Spoon cocktail sauce into a small bowl or divide among individual ramekins. Sprinkle 2 teaspoons coarse sea salt on a small plate; rub lemon wedge around rim of serving glasses or ramekins and dip lightly into salt if desired.

Garnish shrimp with lemon wedges and cilantro sprigs. Serve immediately so shrimp remain cold and firm. Leftover shrimp keep refrigerated up to 2 days; discard sauce after 3 days.