Heat treat the flour: Begin by spreading ½ cup extra flour onto a clean, dry baking sheet. Bake it at 300°F (150°C) for 5-8 minutes, stirring every 2 minutes, until it reaches 165°F (74°C). Allow it to cool completely before using.
Cream the butters: In a mixing bowl, combine unsalted butter, granulated sugar, and brown sugar. Beat them together until light and fluffy, being careful not to over-cream to avoid flat cookies.
Add the eggs: Crack in the eggs, one at a time, mixing well after each addition.
Mix dry ingredients: In a separate bowl, whisk together the all-purpose flour, cocoa powder, baking powder, and salt. Gradually add this mixture to the wet ingredients, mixing just until combined.
Fold in chocolate chips: Gently fold in the chocolate chips.
Scoop and bake: Using a cookie scoop, portion out dough balls weighing between 0.7-0.8 ounces onto a lined baking sheet. Bake at 350°F (175°C) for about 10-12 minutes.
Cool the cookies: Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
Prepare the buttercream: While the cookies cool, mix the softened unsalted butter and powdered sugar until creamy. Add heat-treated flour, vanilla extract, and milk, mixing until smooth and spreadable.
Assemble sandwiches: Take a cooled brownie cookie and spread a generous layer of cookie dough buttercream on the flat side. Top with another cookie.