Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper and set it aside.
Mix the dry ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and pumpkin pie spice. Set aside.
Cream the butter and sugars: In the bowl of a stand mixer (or using a hand mixer), beat the butter, granulated sugar, and brown sugar on medium-high speed until light and fluffy, about 3 minutes.
Add wet ingredients: Add the pumpkin purée, egg, and vanilla extract to the creamed mixture. Mix until fully combined, scraping down the sides and bottom of the bowl as needed.
Combine wet and dry: Add the flour mixture to the wet ingredients and mix just until combined. The dough will be soft and slightly sticky.
Scoop and bake: Using a medium cookie scoop or a spoon, scoop heaping tablespoons of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake: Bake in the preheated oven for 13 to 15 minutes, or until the edges are set and the cookies are soft and fluffy. Let cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
Cream Cheese Frosting:
In a mixing bowl, beat the cream cheese and butter together on medium-high speed until smooth, about 30 seconds.
Add the vanilla extract and sifted confectioners’ sugar. Mix again until just combined, about 30 more seconds.
Once the cookies are completely cooled, frost them using an offset spatula or a knife. Sprinkle lightly with cinnamon, if desired, and serve.