Add the eggs to a large mixing bowl. Use a potato masher to 'smash' them into tiny pieces.
In a separate bowl, use a spatula to toss the onion, celery, relish, Worcestershire sauce, sugar, mustard, garlic powder, salt, and pepper together until evenly combined.
Transfer the mixture to the bowl with the smashed eggs. Use a spatula to stir, until evenly combined and the mixture's smooth. Fold in the mayo, adding more or less to texture/taste, until the mixture's reached your desired creaminess.
Serve this salad on sandwiches, with crackers, or even in lettuce wraps. Sprinkle it with smoked paprika before serving.