Halve the eggs lengthwise and pop the yolks from the whites. Set the whites aside, rounded side up on a plate. Mix the yolks with the mayonnaise and Worcestershire sauce in a medium bowl until the mixture is smooth and light. Add the celery, pickle, parsley, and season with the salt and hot sauce.
Spoon the yolk mixture back into the whites and sprinkle with paprika. Serve now or cover and refrigerate until ready to serve.