Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
In a large bowl, combine flour, oats, baking powder, baking soda, salt, cinnamon and pumpkin pie spice. Mix together until well combined. Set aside.
In the bowl of an electric mixer, combine ¾ C of butter and the brown and white sugars. Cream for about 2 minutes on medium speed. Scrape down the bowl.
Add the egg yolk and beat for 60 seconds on medium speed.
Add the vanilla, molasses and pumpkin. Beat again for about 60 seconds until combined. Scrape down the bowl.
Turn your mixer to the lowest setting and slowly pour in the dry ingredients. Stir until just incorporated. Remove from the mixer. If there are any remaining flour bits, fold them in by hand with a spatula. Let the batter refrigerate for 15 minutes before baking.
Make golf ball sized scoops of dough and place on the prepared baking sheets, leaving about 2 inches space between. Flatten slightly with your fingers, so they are small, thick discs.
Bake for 8-9 minutes, do not over bake. Remove when the edges are barely set when tested with a finger poke. The centers will appear undercooked but not raw. Cool for 5 minutes on the baking sheet them move to a wire rack to cool completely.
For the icing
Add room temperature butter to the bowl of an electric mixer. Beat on medium speed for 2 minutes, until smooth. Scrape down the bowl.
Add the powdered sugar and mix on low until the ingredients are combined. Once they start to come together as a paste, add the vanilla and milk. Mix until combined and scrape down your bowl.
Turn the mixer to medium high speed and beat for 5 minutes. You will notice the icing getting fluffier as time passes.
Remove from the stand and scoop tablespoon amounts of icing onto half of the cookies. Top with the second half making a sandwich. Gently press the two cookies together to spread the frosting out to the edges.
If your icing is very soft, refrigerate your cookies for an hour to set the frosting.
Store cookies in an airtight container at room temperature.