Preheat oven to 350℉.
In a medium mixing bowl, combine oat flour, baking soda, salt, and pumpkin pie spice. In a separate large bowl, mix together pumpkin purée, butter, sugar, brown sugar, and vanilla extract.
Add the dry mix to wet mix and combine. Fold in oats thoroughly.
On a lined baking sheet, scoop dough (2 tbsp each) and flatten slightly with your fingers or the bottom of a bowl.
Cookies will bake for 9-11 minutes. Remove from heat and set aside to cool.
To make the filling, add softened butter to a large mixing bowl. Beat for 2-3 minutes until smooth. Add in powdered sugar, pumpkin pie spice, and mix well. Add milk if necessary starting with 1 tsp.
To assemble, spread or pipe filling on the bottom of one cookie and top with another.
Enjoy!