Preheat your oven to 350°F and line baking sheets with parchment paper.
Cream butter and both sugars until fluffy. Add in pumpkin, egg, and vanilla extract, mixing until smooth.
In another bowl, combine flour, baking soda, baking powder, pumpkin spice, and salt. Gradually add dry ingredients to the wet, mixing just until combined.
Scoop the dough onto the prepared baking sheets. I like using a cookie scoop to keep things even.
Bake for 12-14 minutes or until the cookies are just slightly golden on the edges. Let them cool on a rack.
While they cool, make the icing. Mix the cream cheese and butter until smooth. Add in powdered sugar, vanilla, and milk. Adjust the milk if it’s too thick.
Once the cookies have cooled, spread that dreamy cream cheese icing on top.