Place oven racks on the on the upper and lower third of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment paper.
In a stand mixer fitted with the paddle attachment (or using a bowl and an electric hand mixer), cream the butter, brown sugar and granulated sugar together on high speed until light and fluffy, 3-5 minutes. Scrape down the bowl, turn the speed to low, and add the eggs, one at a time, followed by the vanilla. Scrape down the bowl as needed.
In a medium-sized bowl, whisk together the flour, baking soda, cinnamon, and salt. On low speed, add the flour mixture to the mixer, then add the oats and mix until just combined.
Use a medium-sized scoop (1 1/2 tablespoons) to portion out the cookie dough onto the prepared sheets. Bake until the edges are just starting to brown, 9-11 minutes. They might look slightly underbaked in the center but will continue to set as they cool.
Let the cookies cool for 5-10 minutes, then transfer to a cooling rack to cool completely.
While the cookies cool, prepare the filling. In a stand mixer fitted with the paddle attachment (or using a bowl and electric hand mixer), combine the butter and confectioners' sugar on low speed (add the sugar in a few batches), gradually increasing to high speed until the mixture is light and fluffy. Add 2 tablespoons heavy cream along with the vanilla and salt. If desired, add additional cream to thin out the filling. Transfer the mixture to a piping bag with a round tip.
To assemble the cookies, pipe the filling onto the bottom side of one of the cooled cookies, then place a second cookie on top to create a sandwich. Repeat with the remaining cookies and filling. If you don’t have a piping bag, you can spread the filling onto the cookies with a butter knife.