Preheat the oven to 350°F. Line two cookie sheets with parchment paper.
In a medium bowl, whisk together the flour, baking soda, baking powder, salt, and cinnamon.
In a large mixing bowl, beat the salted butter, granulated sugar, and brown sugar on medium speed for two to three minutes.
Add the egg and vanilla extract. Mix until smooth, scraping down the sides and bottom of the bowl as needed.
Add the dry ingredients and mix on low speed just until combined.
Add the quick oats and mix just until evenly distributed.
Use a cookie scoop to portion level tablespoons of dough onto the prepared baking sheets. Leave about two inches between each cookie.
Bake for 8 to 10 minutes. The edges should be set, but the centers should still look soft.
Cool the cookies on the baking sheet for five minutes. Transfer them to a wire rack and let them cool completely.
To make the filling, beat the unsalted butter until smooth. Gradually add half of the powdered sugar and mix until combined. Add the remaining powdered sugar, salt, vanilla and milk or cream. Mix until well combined and light and fluffy.
Pair the cooled cookies by size. Pipe or spread the butter filling onto the flat side of one cookie.
Top with a second cookie and press gently until the filling spreads close to the edges.