In a saucepan, combine all the ingredients for the court bouillon. Bring to a boil and reduce to simmer for 30 minutes. Strain off any solids and return liquid to saucepan. Check and maintain temperature between 125-135 degrees for poaching.
Lower shrimp into prepared court bouillon and poach shrimp until just cooked, approximately 3-4 minutes. Remove shrimp from liquid and let cool to the touch, then remove peel. Chill shrimp for service.
In a blender or glass measuring cup, combine all ingredients for the cocktail sauce. Using an immersion or stand blender puree all the ingredients. Taste and season with additional pepper or hot sauce to your desired tastes.
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Retain the prepared court bouillon for your future seafood poaching needs, or as stock for soups. Will hold for 5 days under refrigeration.