Prepare the Shrimp: In a large pot, bring about 4-6 cups of water to a rolling boil. Add the juice of one lemon half and a pinch of salt. Carefully add the shrimp to the boiling water. Cook for just 2-3 minutes, or until the shrimp turn pink and opaque and float to the surface. Be careful not to overcook!

Chill the Shrimp: Immediately drain the shrimp using a colander. Plunge them into a bowl of ice water (or run under cold water) to stop the cooking process. Once cooled, drain thoroughly and pat them dry with paper towels.

Make the Cocktail Sauce: While the shrimp are chilling, whisk together the ketchup, horseradish, Worcestershire sauce, hot sauce, Dijon mustard, salt, and pepper in a medium bowl. Taste and adjust seasonings as needed. For a smoother sauce, you can blend it briefly.

Assemble the Cocktail: Arrange the chilled shrimp on a platter, either in a decorative pattern or piled loosely. You can serve them with the tails on for a more classic presentation. Place the bowl of cocktail sauce in the center of the platter or in a small serving dish alongside the shrimp.

Serve: Serve immediately with plenty of ice to keep the shrimp perfectly chilled. Garnish with lemon wedges and optional fresh parsley.