Place eggs in a large pot of cool water. Bring water to a boil. Let water boil for 10 to 15 minutes.
Plunge the eggs in cold water. When eggs are cool enough, remove their shells and cut them in half lengthwise to remove the yolk. Place the yolks in a medium-size mixing bowl and mash them well.
Mix mustard, Worcestershire sauce, hot sauce, celery salt, and softened butter into the mixing bowl with the yolks. Blend mixture until smooth. Scoop mixture into the hollowed portion of the eggs. Refrigerate one hour and serve.