For the shrimp: Put about 10 cups of water, the carrots, celery, garlic, lemon, onion, parsley, thyme and bay leaves in a large pot and bring to a boil over high heat. Lower the heat to a simmer, set a cover on top slightly ajar, and simmer for 30 minutes.
Careful not to splash, drop the shrimp into the water and turn off the heat. Cook the shrimp, stirring occasionally, until they curl and turn pink, about 2 to 3 minutes for medium shrimp, 4 minutes for large ones. Drain and cool to room temperature. Peel the shrimp and remove the vein along the curve of the shrimp if desired. Refrigerate if not serving right away.
For the Cocktail Sauce: Combine the ketchup, horseradish, Worcestershire and lemon zest and juice in a small bowl. Add hot sauce if using. Mix well, then refrigerate until ready to serve
To serve put the cocktail sauce in a medium bowl and surround with the shrimp, or loop the shrimp over the edge of an individual cocktail glass and top with the sauce. Garnish with the lemon wedges and serve.
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