Preheat the oven to 350°F and line two large baking sheets with parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, or using an electric hand mixer, cream together the butter and brown sugar until well-combined, about 1 minute. Add the egg and mix to combine, followed by the pumpkin puree and vanilla extract.

Sprinkle the pumpkin pie spice, baking powder, baking soda, and salt evenly over the pumpkin mixture. Mix to combine, then add the flour and mix on low speed until just combined, stopping to scrape down the sides of the bowl as needed. The dough will be very soft, like a thick, scoopable batter.

Use a 2-tablespoon cookie scoop to scoop the dough onto the prepared baking sheets, leaving 2 inches between dough balls.

Bake, one sheet at a time, for 12 to 15 minutes, or until the cookies are puffed and the tops are set. Remove from the oven and let cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

When completely cool, frost with cream cheese frosting, if desired.