Fill a large pot with water, add a generous pinch of salt, and bring to a rolling boil over high heat.
Once boiling, add the large shrimp carefully using a slotted spoon, and cook for about 2-3 minutes until they turn bright pink and are just firm to the touch.
While the shrimp cook, prepare the cocktail sauce by combining ketchup, horseradish, lemon juice, Worcestershire sauce, and hot sauce in a small saucepan. Gently warm the mixture over low heat, stirring until smooth and fragrant.
Once the shrimp are cooked, quickly transfer them into a bowl of ice water to stop the cooking process and help them chill thoroughly. Let them sit for at least 10 minutes until very cold and firm.
Drain the shrimp well and pat dry with paper towels. Arrange them neatly in serving glasses or bowls, tails up for an attractive presentation.
Squeeze fresh lemon over the chilled shrimp for a bright, citrus aroma, and sprinkle with chopped herbs for a fresh pop of color and flavor.
Serve the shrimp with the slightly cooled cocktail sauce on the side, garnished with additional lemon wedges if desired.
Encourage guests to dip the chilled shrimp into the tangy sauce and squeeze extra lemon for a burst of fresh flavor in each bite. Enjoy immediately for the best texture and flavor.