Make the cocktail sauce first so it has time to chill and the flavors meld. In a small mixing bowl, stir together the 1 cup ketchup, 2 tbsp prepared horseradish or more, 1 tbsp fresh lemon juice, 1 tsp Worcestershire sauce, ½ tsp hot sauce such as Tabasco, and 1 tbsp kosher salt. Taste and adjust — add more 2 tbsp prepared horseradish or more for extra kick or more 1 tbsp fresh lemon juice for brightness. Cover and refrigerate until ready to serve.

Fill a large pot with 3 quarts of quarts water. Add the 1 tbsp kosher salt, 1 tsp black peppercorns whole, smashed 2 cloves garlic smashed, 2 stalks celery roughly chopped, 2 whole bay leaves, and squeeze in the 1 lemon halved halves, then drop them in too. Bring to a rolling boil over high heat.

While the water heats, prepare an ice bath: fill a large mixing bowl with plenty of crushed ice for chilling and presentation and 3 quarts water. Set it near the stove.

Once the water is at a full boil, reduce the heat to medium so it settles to a gentle simmer. Add all the large shrimp peeled and deveined in a single batch. Poach, stirring once, until the 2 lb large shrimp peeled and deveined are pink, curled into a loose 'C' shape, and just opaque throughout — about 2 to 3 minutes. Do not overcook; they should not curl tightly into an 'O'.

Using a slotted spoon, immediately transfer the 2 lb large shrimp peeled and deveined to the ice bath. Let them chill for at least 5 minutes until completely cold. This stops the cooking instantly and keeps them tender and juicy.

Drain the 2 lb large shrimp peeled and deveined well in a colander and pat dry with paper towels. At this point, the 2 lb large shrimp peeled and deveined can be refrigerated in an airtight container for up to 2 days.

To serve, spread crushed 4 cups crushed ice for chilling and presentation on a large platter or in individual glasses. Arrange the chilled 2 lb large shrimp peeled and deveined over the 4 cups crushed ice for chilling and presentation with their tails hooked over the rim for easy grabbing. Place the cocktail sauce in a mixing bowl in the center (or at the bottom of each glass). Add 1 lemon halved wedges around the platter. Serve immediately.