This is one recipe I get requests for all the time. I can't wait till Fall every year to make it. This is a modified version of a recipe I got from my former professor, Elizabeth at Duke University Physical Therapy School. Thanks Elizabeth!
Preheat oven to 375. Sift together the first five dry ingredients and set aside. Cream the butter well and add the sugar, pumpkin, egg, and last the vanilla. Add the dry to the wet ingredients. Bake on non-stick or greased cookie sheet for about 10 minutes until done. Allow to cool completely before frosting.
To make frosting combine the butter, brown sugar and milk in a small sauce pan. Boil exactly 2 minutes, stirring as it cools. When nearly cool, whisk in powdered sugar and vanilla. Frost quickly as it becomes firm quickly. Frequently a put it in a small pitcher and drizzle it over the cookies. If it becomes to firm, add a small splash of milk and stir.