Fill a large pot with water, add the lemon halves, bay leaves and peppercorns, and bring to a boil over high heat.

Add the shrimp and cook for 2 to 3 minutes, until they turn pink and curl into a loose C shape.

Drain immediately and plunge the shrimp into a bowl of ice water to stop the cooking.

Once cold, drain the shrimp and pat dry, then refrigerate for at least 30 minutes.

Toss the diced avocado with lime juice in a small bowl to keep it from browning.

Stir together the ketchup, horseradish and hot sauce in a bowl to make the cocktail sauce; taste and add more horseradish for extra bite.

Spoon the cocktail sauce into a serving glass or small bowl and set it in the center of a platter.

Arrange the chilled shrimp around the sauce, hooking each tail over the rim of the glass.

Scatter the avocado and cilantro over the top and serve with lime wedges.