Preheat the oven to 350 degrees F and line a large baking sheet with a silpat mat or parchment paper.

In a large bowl, beat the butter, granulated sugar, and brown sugar together until well-mixed. If using a stand mixer, make sure to use the paddle attachment. 

With the mixer on low speed, add the egg, pumpkin puree, and vanilla extract. 

With the mixer on low speed, slowly add the flour, pumpkin pie spice, and baking soda.  Mix just until combined, you don’t want to overmix! 

Scoop out 1-inch balls of dough onto the prepared baking sheet, making sure to place them at least 2 inches apart. Press each of the cookies down gently to flatten them slightly. 

Bake until the edges are golden brown and the center is set, about 10-12 minutes. 

Transfer the cookies to a wire rack to cool while you make the icing. 

Beat the softened cream cheese on medium speed until smooth, about 30 seconds. 

With the mixer on low, slowly add the powdered sugar, about ¼ cup at a time. 

When the sugar has been fully incorporated, add the vanilla and mix to combine. Scrape down the sides of the bowl as needed. 

Frost each of the cookies with 1 tablespoon of icing and top with a pinch of pumpkin pie spice if desired.

Store leftover cookies in an airtight container in the fridge for up to two days.