Preheat oven to 350 degrees. Line light colored baking sheets with parchment paper and set aside.
In a large bowl, whisk dry ingredients until combined. Set aside.
Cream butter and sugar together in the bowl of a stand mixer. Add in pumpkin, egg and vanilla until well incorporated. Scrape sides of bowl and mix again to ensure it was evenly mixed.
Slowly incorporate dry ingredients into the dough until just combined.
Using a cookie scoop, portion dough onto baking sheets and bake 12-15 minutes or until cookies are puffed and bottoms are lightly browned.
Cool 5 minutes on baking sheets before transferring to cooling racks.
For the glaze, whisk powdered sugar together with vanilla and milk. Add in enough milk to get the glaze the consistency of white school glue. Drizzle over cookies. Glaze should dry after 10-20 minutes.
Store in air tight containers for up to 3 days at room temperature, 5 days in the refrigerator.
After a quick google search, I realized that this "family" recipe is extremely similar to the one over at Very Best Baking. While I don't credit them per say, it's important to recognize that similarity.