Preheat the oven to 350º F (180º C). Line two baking sheets with parchment paper.
Combine flour, baking soda, baking powder, pumpkin pie spice, and salt in a medium bowl.
Using an electric hand mixer or a stand mixer, cream butter and sugar until light and fluffy, about 3 minutes. Beat in pumpkin puree, cream cheese, and vanilla extract; mix until well incorporated. Scrape down the sides and bottom of the bowl as needed.
Add the dry ingredients to the bowl, then mix on low until combined.
Drop dough onto prepared baking sheets by tablespoonfuls; flatten slightly with fingers. TIP: For evenly sized cookies (better for baking), use a small spring-loaded ice cream scoop to spoon out the dough.
Bake for 15 to 18 minutes or until very lightly browned on the sides. The centers will look very soft. Cool on pan 5 minutes before removing to wire racks to cool completely. Drizzle glaze over cooled cookies, if desired.