Who doesn't love shrimp cocktail? It always scores major fancy points but couldn't be easier to make--even when you concoct your own cocktail sauce. The cardinal sin of shrimp cocktail is serving mealy, overcooked shrimp; cooking them with the peel on will help prevent them from overcooking. Also, leave enough time to chill the shrimp well—it's important to serve them to your guests ice cold!
For the shrimp: In a wide, shallow pan, combine the lemon, peppercorns, bay leaves, wine, and salt. Bring the poaching liquid to a gentle simmer over low heat. Add the shrimp and poach them for 3 to 5 minutes, or until they turn pink. Drain the shrimp and let them cool until they're cool enough to handle.
Peel the shrimp, leaving the tails on.
Look for the dark "vein" that runs the length of the shrimp's back. In order to remove it without destroying the shrimp, I recommend laying the shrimp on its side and carefully running a sharp paring knife down its back to make a shallow cut. Use the tip of the knife to extract the exposed vein.
Refrigerate the shrimp until you're about to serve them.
Meanwhile, in a medium bowl, whisk together the ketchup, pepper, lemon juice, and horseradish to make the cocktail sauce. Taste the sauce and season with more horseradish if you want to add extra kick. Refrigerate.
Serve both the shrimp and cocktail sauce very cold.