In a large pot combine 6 cups water, kosher salt, granulated sugar, bay leaves, black peppercorns and the juice of 1 lemon (reserve used lemon halves). Bring to a gentle boil over medium-high heat.

Cook shrimp

Add the peeled and deveined shrimp to the gently boiling liquid in a single layer. Return to a boil, then reduce heat so liquid very gently simmers. Cook until shrimp are opaque and just curled, about 2 to 3 minutes depending on size. Do not overcook.

Shock shrimp

While shrimp cook, prepare an ice bath: a large bowl with 4 cups ice and some cold water. As soon as shrimp are cooked, transfer them with a slotted spoon into the ice bath to stop cooking. Chill until completely cool, about 5 minutes. Drain well and pat dry with paper towels. Refrigerate until serving.

Cocktail sauce

In a medium bowl combine 1 cup ketchup, 3 tsp prepared horseradish (start with less and add more to taste), 1 tbsp lemon juice, 1 tsp Worcestershire sauce, 1 tsp hot sauce (optional), 1 tsp smoked paprika, 1 tsp salt and 1 tsp freshly ground black pepper. Whisk until smooth and taste; adjust horseradish, lemon, salt or hot sauce as desired. Chill in refrigerator for at least 15 minutes to let flavors meld.

Garnish & serve

Arrange a shallow serving bowl or platter with a bed of ice. Place chilled shrimp around the rim or stacked over the ice with tails out for easy grabbing. Put cocktail sauce in small ramekins in the center or distributed around the platter.

Garnish with lemon wedges and sprinkle chopped parsley over shrimp. Provide cocktail forks or toothpicks. Serve immediately while shrimp are cold.