To make the court bouillon: Combine the water, carrot, celery, onion, parsley, thyme, and bay leaf in a large pot and bring to a boil. Lower the heat to a simmer, set a cover on top slightly ajar, and cook for 30 minutes.
Meanwhile devein the shrimp. Hold a shrimp between the thumb and forefinger with the rounded side of the shrimp upward. Place the pointed end of a wooden skewer at the junction of the second and third segments of the shrimp shell, about 1/8 of an inch down from the top. Gently push the skewer through the shell, so it crosses the shrimp right under the vein. Place you forefinger over the spot the vein and skewer meet, and gently pull the skewer up to remove the vein. Repeat with the remaining shrimp.
Strain the court bouillon into a bowl and then return to the large pot. Bring to a boil and add the salt. Drop the shrimp into the liquid and turn off the heat. Cook the shrimp, stirring occasionally, until they curl and turn pink, about 2 to 2 1/2 minutes for medium shrimp, 3 minutes for large ones. Drain and cool to room temperature. Peel the shrimp if desired. Refrigerate the shrimp if not serving right away.
If refrigerated, bring the shrimp to room temperature 20 minutes before serving. Put the cocktail sauce in a medium bowl and surround with the shrimp, or loop the shrimp over the edge of a individual cocktail glass and top with the sauce. Garnish with the citrus wedges and serve.
Combine the ketchup, lemon zest and juice, horseradish, and Worcestershire sauce in a small bowl. Add hot sauce, if desired. Mix well, then refrigerate until ready to serve.
Yield: 1 1/2 cups
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From Food Network Kitchens