Preheat the oven to 350°F. Line two baking sheets with parchment paper.
Place the pumpkin puree between several layers of paper towels and gently press to remove excess moisture
In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, and pumpkin pie spice.
In the bowl of a stand mixer fitted with the paddle attachment, beat the softened butter, brown sugar, and granulated sugar on medium speed for 2 to 3 minutes, or until creamy.
Add the egg yolk and vanilla extract and mix until combined.
Add the blotted pumpkin puree and mix just until evenly incorporated.
Add the flour mixture and mix on low until most of the flour has disappeared.
Add the quick oats and mix just until evenly distributed.
Use a #20 cookie scoop to portion the dough onto the prepared baking sheets, leaving about 2 inches between each cookie. Press the tops down very slightly only if needed. Bake for 8 to 10 minutes, or until the edges are set and the centers still look soft.
While the cookies are still warm, use a round cookie cutter slightly larger than the cookies to gently shape them into even circles.
Cool on the baking sheet for about 5 minutes, then transfer to a wire rack to cool completely.
To make the buttercream, beat the softened butter until smooth. Gradually add the powdered sugar, vanilla, salt, and 4 tablespoons of cream or milk.
Beat until smooth and fluffy, adding a little more powdered sugar if you want a firmer filling or a small amount of additional cream if needed.
Pair cooled cookies by size. Pipe buttercream onto the flat side of one cookie and top with a second cookie. Press gently until the filling reaches toward the edges.