Preheat oven to 375 degrees and prepare a baking sheet by lining it with parchment paper.
Cream butter, shortening and vanilla until fluffy.
Add sugars, molasses, egg, and pumpkin and mix until combine.
In a separate bowl, whisk together flour, salt, baking soda, cinnamon, and pumpkin pie spice.
Add the dry ingredients to the pumpkin mixture and beat until combine.
Stir in oats.
Place tablespoon size balls of dough on the parchment paper lined cookie sheet.
Bake for 12 to 15 minutes or until the edges of the cookies are brown but the middles are still soft.
To make the filling, cream the butter, vanilla, and pumpkin pie spice together until light and fluffy. Add the powdered sugar and milk, alternating one cup sugar and one tablespoon milk until icing reaches the desired consistency.
1Pipe icing into the middle of 15 cookies when the cookies are completely cooled, then top each with another cookie.