Hard boil the eggs in water and a bit of vinegar (about 8–10 minutes after water boils). Run under cold water for about 5 minutes, then peel. Slice the eggs in half lengthwise and remove the yolks. Mash the yolks and add mayonnaise and Worcestershire sauce. Stir in onion, mustard, pickle, parsley, salt, and horseradish.
Arrange the cooked egg whites on a platter, or egg plate if available. Scoop a generous portion of the yolk mixture into each white, and sprinkle with Old Bay seasoning. Place an olive half on top of each egg. Best if served cold.