Preheat oven to 350 °F (177 °C) and line baking sheets with parchment paper or silicone baking mats.
In a large bowl, whisk together flour, baking soda, baking powder, pumpkin pie spice, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together butter and sugars until light and fluffy. Next, add the egg and vanilla extract and mix until incorporated.
Add the pumpkin puree and peanut butter and beat until mixed well. Then gently add in the flour mixture in two batches.
Spoon dough onto cookie sheet with a cookie scoop.
Bake for 10-12 minutes or until edges start getting golden brown and the cookie is just starting to set.
Let cool on baking sheet for 5 minutes before transferring to a wire cooling rack to cool completely.