For the cookies:
1 1/2 cups rolled oats (not instant)
3/4 cup all-purpose flour
3/4 teaspoon ground cinnamon
1/2 teaspoon baking powder
1/4 teaspoon fine salt
8 tablespoons (1 stick) unsalted butter, at room temperature
1/3 cup packed dark brown sugar
1/4 cup granulated sugar
1 tablespoon molasses (not blackstrap)
1 large egg
1/2 teaspoon vanilla extract
For the filling:
2/3 cup powdered sugar, sifted
3 tablespoons unsalted butter, at room temperature
1 tablespoon heavy cream
1/4 teaspoon vanilla extract
Pinch fine salt
For the cookies: Arrange 2 racks in the oven to divide it into thirds and heat to 350°F. Line 2 baking sheets with parchment paper; set aside.
Whisk the oats, flour, cinnamon, baking powder, and salt together in a large bowl; set aside.
Place the butter, sugars, and molasses in the bowl of a stand mixer fitted with the paddle attachment and mix on medium speed until fluffy and lightened in color, about 3 minutes. Add the egg and vanilla and beat until incorporated.
Stop the mixer and scrape down the sides of the bowl and paddle. With the mixer on low, gradually add the oat mixture until just combined (do not overmix).
Drop the dough by level tablespoons onto the baking sheets, spacing them about 1 inch apart (up to 24 per baking sheet). Bake for 7 minutes. Rotate the baking sheets between racks and from front to back, then bake until the cookies are light golden-brown on the edges, 5 to 6 minutes more.
Let the cookies cool on the baking sheets for 2 minutes, then transfer to a wire rack to cool completely. While the cookies are cooling, make the filling.
For the filling: Place the powdered sugar and butter in the clean bowl of the stand mixer fitted with the paddle attachment and beat on low speed until combined, about 1 minute. Increase the speed to medium-high and beat until fluffy and smooth, about 2 minutes more.
Stop the mixer and scrape down the sides of the bowl and paddle with a rubber spatula. Add the cream, vanilla, and salt, and beat on medium-high speed until incorporated and you achieve a fluffy, spreadable texture, about 1 minute more. Transfer the filling to a plastic sandwich bag or disposable piping bag.
Assemble the cookies: Flip half of the cookies over. Snip a corner off the bag of filling. Pipe the filling onto the flipped cookies and spread into an even layer, leaving a 1/4-inch border. Top with the remaining cookies to create sandwich cookies.