Fill a large pot with the water and add in onion, celery, garlic, bay leaves, peppercorns, chile pepper, lemon, parsley, thyme, and a large handful of salt (the water should approximate sea water in saltiness).
Bring to a hard boil, then reduce to a simmer, cover, and cook for 15-20 minutes.
Add the shrimp and increase heat to high; once the court bouillon has returned to a simmer, remove from the heat and set aside, covered, for 5 minutes.
Drain the shrimp in a colander, reserving the court bouillon for another use.
Transfer the shrimp to a small baking sheet and refrigerate.
When the shrimp are cool, peel and devein.
Cocktail sauce-combine all the ingredients in a small bowl; taste and adjust the seasoning, adding more horseradish, hot sauce and/or lemon or lime juice to taste.
Transfer to a small serving bowl.
To serve, put the bowl of cocktail sauce in the center of a serving plate and arrange the shrimp and lemon wedges around it.