Boil the eggs by placing them in a saucepan, covering with cold water, bringing to a boil, then letting sit covered for 12 minutes. Transfer to ice water for 5 minutes to cool.
Peel the eggs under running water, slice in half, and remove yolks to a mixing bowl.
Add pumpkin puree, mayonnaise, Dijon mustard, apple cider vinegar, pumpkin pie spice, salt, and pepper to the yolks. Mix until smooth and creamy.
Fill the egg whites with the yolk mixture using a spoon or piping bag.
Garnish with fresh parsley or chives and serve immediately or refrigerate until ready to serve.