Step 1

For the dressing: Whisk together the mayonnaise, ketchup, horseradish, lemon juice, sugar, vinegar, Worcestershire and a pinch each of salt and pepper in a small bowl until smooth. Refrigerate until ready to use.

Step 2

For the salad: To make medium-boiled eggs, put the eggs in a small saucepan and cover with cold water. Bring to a boil, then remove from heat, cover and let stand 5 minutes. Transfer to an ice bath. Remove the shells once cool and quarter each egg lengthwise.

Step 3

Heat a large skillet over medium high. Put the shrimp to a medium bowl, sprinkle with the Old Bay Seasoning and toss to coat. Swirl the oil into the skillet, then stir in the shrimp and cook, tossing occasionally, just until pink and firm, 3 to 4 minutes. Transfer to a large bowl and reserve.

Step 4

Put the lettuce, tomato, cucumber and avocado in a second large bowl. Season with 1 pinch each salt and pepper. Dress with about 1/2 cup of the dressing and toss gently to coat the vegetables. Divide onto 4 plates and arrange the shrimp and medium-boiled eggs on top before serving. Serve the remaining dressing on the side.