Preheat oven to 350 degrees F and grease an 8x8 pan.
With a stand mixer, or handheld electric mixer, mix together butter and sugar on low speed for about 30 seconds.
Add egg, vanilla, and pumpkin puree, and beat for about 1 minute, until well combined.
In a separate bowl, whisk together the flour, baking powder, salt, and pumpkin pie spice. Need a recipe for pumpkin pie spice? Try ours! Homemade Pumpkin Spice - Just Give Us The Recipe Gradually add the flour mixture to the pumpkin puree mixture while beating on medium speed, just until combined.
Bake for 30 minutes, or until toothpick inserted comes out clean. Allow to cool.
For the glaze, add powdered sugar to a bowl with milk and vanilla. Beat with a whisk attachment until there are no clumps visible.
Use a toothpick to poke holes throughout the top of the bars. Pour glaze over and slice to desired size. Enjoy!