Make the cookies: Preheat the oven to 350°F and set aside 1-2 lined baking sheets.
Whisk together the flour, baking soda, salt, and pumpkin spice in a medium mixing bowl.
In a separate, large bowl, beat the pumpkin puree, butter, sugars, and vanilla.
Add the dry mixture to the wet and mix until just combined.
Fold in the oats.
Use a scooper to place rounded scoops of dough (about 2 tbsp each) on a lined baking sheet. Flatten each slightly using your fingers or the bottom of a cup.
Bake for 9-11 minutes. Set aside to cool completely.
Make the buttercream: Add the butter to a large mixing bowl and beat for about a minute.
Add in the powdered sugar and pumpkin spice and continue to beat for another minute or so.
Add milk, as necessary, to reach the desired consistency.
Assemble: For each pie, spread or pipe the frosting on the bottom of one cookie and top with another cookie. Enjoy!
