Preheat oven to 350°F and line a baking sheet with parchment paper.

In a large bowl, beat the butter on medium-high speed for about 1 minute until smooth. Add the sugar, baking powder, baking soda, salt, cinnamon, and pumpkin pie spice. Beat until well combined, scraping down the sides as needed.

Add the egg and vanilla extract. Beat until fully incorporated and no streaks remain. Mix in the blotted pumpkin puree until combined.

With the mixer on low speed, gradually add the flour. Increase speed slightly and mix until fully incorporated. The dough will be soft and slightly wet.

Scoop heaping tablespoons of dough onto the prepared baking sheet, spacing them a few inches apart. Bake for 10 to 12 minutes, or until the tops are set and no longer look wet.

Allow the cookies to cool on the baking sheet for a few minutes, then transfer them to a wire rack to cool completely.

To make the frosting, beat the butter and cream cheese together until smooth and creamy. Sift in the powdered sugar, add the vanilla, and beat until light and fluffy. Frost the cooled cookies generously.