Using a mixer, beat the butter until smooth. Beat in the white and brown sugars, a little at a time, until the mixture is light and fluffy. Beat in the egg, then mix in the vanilla and pumpkin puree. In a large bowl, whisk together the flour, baking soda, salt, cinnamon, and pumpkin spice. Slowly beat the flour mixture into the batter in thirds. Stir in the chips.
Preheat oven to 350 F degrees. Line cookie sheets with parchment paper.