Make the brine: In a large bowl, whisk together the water, salt, and sugar until dissolved. Add the shrimp and ice and let soak for 20 to 30 minutes. Drain.
Meanwhile, make the court bouillon: In a large saucepan, combine the water, salt, peppercorns and bay leaves. Squeeze the lemon juice into the water, add the lemon halves, and bring to a boil
Add the shrimp to the water and cook until they just turn opaque, about 3 minutes. Drain the shrimp, transfer to a baking sheet, and let cool.
When the shrimp are cool enough to handle, peel and de-vein them and chill in the refrigerator.
When ready to serve, divide the cocktail sauce among 4 martini glasses and hang the shrimp around the rims. Serve immediately.
In a medium bowl, whisk together all the ingredients. Store in the refrigerator until ready to serve.