In a large pot bring 2 liters of water to a simmer. Add kosher salt, black pepper, bay leaf and the halved lemon (squeeze one half into the water, then add the rinds). Maintain a gentle simmer—do not boil vigorously.

Poach shrimp

Add the peeled and deveined shrimp in a single layer. Cook just until the shrimp turn opaque and curl into a loose 'C' shape, about 2 to 3 minutes depending on size. Overcooking will make them tough.

Shock shrimp

Immediately transfer the cooked shrimp with a slotted spoon into a large bowl filled with the ice and enough cold water to cover (ice bath). Let sit 3 minutes to stop cooking and chill completely.

Dry and chill

Drain shrimp well on paper towels, pat dry, and refrigerate on a plate covered loosely with plastic wrap until ready to serve (at least 15 minutes). Keep tails on for presentation.

Remoulade Sauce

Combine base ingredients

In a medium bowl whisk together mayonnaise, Dijon mustard, whole grain mustard, prepared horseradish and ketchup until smooth.

Add aromatics and seasonings

Stir in finely minced shallot, minced garlic, pickle relish, chopped capers, lemon juice, Worcestershire sauce and hot sauce. Mix to combine.

Finish and adjust

Add paprika, smoked paprika, chopped parsley, salt and black pepper. Taste and adjust for acidity, heat or salt—add up to 1 tsp more lemon juice, a pinch of sugar if needed, or more hot sauce to taste. Cover and refrigerate at least 30 minutes to allow flavors to meld.

Garnish & Serving

Assemble platter

Spread crushed or shaved ice on a large serving platter or individual cocktail glasses. Spoon the remoulade into a small bowl placed centrally (or into individual ramekins). Arrange shrimp around the bowl in a fan so tails rest on the ice for presentation.

Serve

Garnish with lemon wedges and parsley sprigs. Offer additional cocktail sauce at the table if desired. Keep the platter chilled and serve immediately so shrimp remain cold and the remoulade retains texture.

Make-ahead note

Remoulade can be made up to 48 hours ahead and refrigerated. Poach shrimp up to 4 hours before serving, keep chilled on ice. Assemble just before serving for best texture.