Defrost the Shrimp - If using frozen shrimp, defrost in the refrigerator overnight, about 24 hours. For quick defrosting, place them in a colander and run cold water over them until they are no longer icy, about 10 minutes.
Peel and Devein - Use kitchen shears to cut through the top of the shell. Remove the shell but leave the tail on. Use a paring knife to cut a shallow line down the back and remove the dark digestive tract. In a colander, wash and then drain.
Poach the Shrimp - In a large pot or Dutch oven, add 8 cups of water, salt, lemon peel, and bay leaves. Heat over medium heat, stirring to dissolve the salt. Heat until the surface is just beginning to move but not bubbling. The temperature should be about 180°F (82ºC), about 10 minutes.Add the shrimp to the pot, stir, and cook until opaque, loosely curled, and the thickest part reaches 140ºF (60ºC), about 2 ½ to 3 ½ minutes.
Add Shrimp to the Ice Bath - In a large bowl, add 4 cups of cold water and 4 cups of ice. Immediately transfer the shrimp to the ice water bath. Chill until cool, about 5 minutes. Drain using a colander.
Make the Cocktail Sauce - In a medium bowl, whisk together the tomato paste, water, lemon zest, lemon juice, honey, horseradish, Worcestershire sauce, hot sauce, salt, garlic powder, onion powder, and vinegar. Taste and adjust seasoning as desired. Transfer to a bowl for serving.
To Serve - Place the cooked shrimp on top of a bowl of ice or a serving platter (no ice if eaten immediately). Garnish with lemon wedges and serve with a bowl of cocktail sauce.
Notes
Serving Size: 1 shrimp plus about 1 teaspoon sauce
Cocktail Sauce Yield: About 1 cup
Make ahead: Cooked shrimp can be and stored in an airtight container in the refrigerator for up to 1 day in advance. The sauce can be stored in the refrigerator for up to 2 days.