Cut hard-cooked eggs in half lengthwise.
Remove egg yolks; set egg whites aside.
In a small bowl, use a fork to mash egg yolks.
Stir in mayonnaise, mustard, vinegar, salt, pepper and celery seeds, if desired.
Spoon egg yolk mixture evenly into egg white halves.
Arrange on a small platter.
Garnish with parsley.