Preheat the oven to 350 degrees. Combine flour, Baking soda, Baking powder, cinnamon, nutmeg, and salt in a medium bowl and set aside.
In your mixer, cream together the butter and white sugar.
Add pumpkin, egg, and vanilla to the butter mixture, and beat until it is creamy.
Add all of the dry ingredients gradually and beat until combined.
Drop on cookie sheet by tablespoonfuls. The dough will be pretty soft.
Bake in the oven for 15 to 20 minutes.
In another bowl, add the cream butter and cream cheese together in the mixer. Slowly add the powdered sugar and mix until it is thick and creamy; then add the vanilla into the mixture.
When the cookies are cooled, spread the frosting on top of the cookie with a spatula.