In a large saucepan or pot, combine 6 cups water, halved lemon, bay leaves, peppercorns, kosher salt, Old Bay seasoning and sugar. Bring to a rolling simmer over medium-high heat, stirring once to dissolve salt and sugar. Once simmering, reduce heat so the liquid stays at a gentle simmer.

Shrimp

Cook shrimp

Add the raw peeled and deveined shrimp to the gently simmering poaching liquid in a single layer. Return to a bare simmer (small bubbles) and cook until shrimp are opaque, pink, and just curled, about 2 to 3 minutes depending on size. Do not overcook; shrimp will continue to cook slightly after removal.

Shock shrimp

Meanwhile, fill a large bowl with the ice and 4 cups cold water to make an ice bath. As soon as shrimp are cooked, use a slotted spoon to transfer them to the ice bath to stop cooking. Let shrimp sit in the ice bath 3 to 5 minutes until fully chilled.

Peel and dry

If shrimp still have tails on and you prefer tails on, leave them. Otherwise remove tails. Pat chilled shrimp dry with paper towels and arrange on a platter or individually portion into cocktail glasses.

Cocktail sauce

Make sauce

In a small bowl, whisk together 1/2 cup ketchup, 2 tsp prepared horseradish, 1 tbsp fresh lemon juice, 1 tsp Worcestershire sauce, 1/2 tsp hot sauce, 1/4 tsp smoked paprika (optional), 1/8 tsp salt and 1/8 tsp freshly ground black pepper. Taste and adjust horseradish or hot sauce to your preferred heat level.

Chill sauce

Cover and refrigerate the sauce until ready to serve so flavors meld (at least 15 minutes).

Plating & garnish

Spoon cocktail sauce into a small bowl or portion into shallow wells of cocktail glasses. Arrange chilled shrimp around the rim or on a platter with sauce in the center. Garnish with lemon wedges and chopped parsley. Serve immediately.