Preheat your oven to 350°F (175°C).
In a large bowl, cream together the butter, brown sugar, and granulated sugar until smooth.
Add the pumpkin puree and egg, mixing until well combined.
In another bowl, whisk together the flour, baking soda, baking powder, pumpkin pie spice, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Scoop tablespoon-sized portions of dough onto a baking sheet lined with parchment paper.
Gently flatten each cookie with the back of a spoon.
Bake for 10-12 minutes until the edges are lightly golden.
Remove from the oven and let cool on the baking sheet for 5 minutes.
Transfer cookies to a wire rack to cool completely.