To Heat Treat the Flour:
Before baking the cookies, heat treat the flour to be used in the buttercream. Spread the flour onto a clean, dry baking sheet. Use 1/2 cup more than the recipe calls for to ensure you have enough.
Bake at 300°F (150°C) for 5-8 minutes, checking every 2 minutes with a digital thermometer. Stir the flour each time you check the temperature and rotate the pan in the oven.
Bake until the temperature reaches 165°F (74°C), then remove from the oven and allow to cool completely.
For the Brownie Cookies:
Place chocolate and butter in a heatproof bowl and set over a double boiler on medium heat. Stir frequently until the chocolate and butter are melted and smooth. Remove from heat and let cool slightly.
In a separate bowl, whisk together the flours, cocoa powder, baking powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the whisk attachment, pour in the slightly cooled chocolate mixture. Add the eggs, brown sugar, and granulated sugar, and mix on medium-low speed until well combined. Add the vanilla extract and mix until incorporated.
Gradually add the dry ingredients to the chocolate mixture, mixing until just combined. Do not overmix.
Cover the bowl with plastic wrap and chill the dough for 30 minutes.
Preheat the oven to 350°F (177°C). Line two baking sheets with parchment paper.
Using a small cookie scoop, measure out dough balls (approximately .07-.08 ounces each). Place the dough balls on the prepared baking sheets, spacing them about 2 inches apart.
Bake for 8-10 minutes, until the edges are set and the centers begin to puff and crack slightly. Do not overbake.
Remove the cookies from the oven. While they are still warm, use the inside arch of a fork to gently nudge the edges toward the center, or swirl a round cookie cutter around the outside to form uniform rounds.
Cool the cookies on the baking sheets for 8-10 minutes before transferring them to a wire rack to cool completely.
For the Cookie Dough Buttercream:
In the bowl of a stand mixer fitted with the paddle attachment, cream together the softened butter and brown sugar on medium-high speed until light and fluffy.
In a small bowl, whisk together the confectioners’ sugar and flour. Gradually add this mixture to the butter and sugar, 1/2 cup at a time, mixing on low speed. Once all the dry ingredients have been added, increase the speed to medium and beat for one minute.
Add the vanilla extract and salt, mixing to combine.
Gradually add the heavy cream, one tablespoon at a time, until the buttercream reaches the desired consistency. The buttercream should be smooth, fluffy, and firm enough to hold its shape when piped.
To Assemble the Sandwiches:
Once the cookies are completely cool, pipe a swirl of cookie dough buttercream onto the flat side of one cookie.
Top with another cookie, flat side down, and gently press together. Optionally, sprinkle with a bit of flaky sea salt.
Refrigerate the cookie sandwiches to set if needed. Serve chilled or at room temperature.