Preheat your oven to 325°F. Line rimmed baking sheets with unbleached parchment paper and set them aside.
In a large bowl, place the flour, cocoa powder, baking soda, baking powder, and salt, and whisk to combine well. Set the dry ingredients aside.
In a medium-size, heat-safe bowl, place the butter and chocolate and melt over a double boiler until smooth. Alternatively, melt in a microwave safe bowl in the microwave in 30-second bursts at about 70% power until melted and smooth.
To the chocolate mixture, add the granulated sugar, egg, egg white, and vanilla, and mix until very smooth.
Create a well in the center of the dry ingredients and add to the wet mixture. Mix to combine, and then knead the dough with your hands to bring it together.
Place the dough between two sheets of unbleached parchment paper and roll it out with a rolling pin until it’s about 1/4-inch thick.
Remove the top sheet of parchment, and cut out rounds using a 2-inch round cookie cutter. Pull away the surrounding cookie dough, and remove the rounds from the paper. Place the rounds 1-inch apart on the prepared baking sheets.
Place the baking sheets, one at a time, in the center of the preheated oven and bake until the cookies are dry to the touch (about 15 minutes).
Remove the baking sheets from the oven and allow the cookies to cool completely on the baking sheets. They will crisp as they cool.
Prepare the filling
In the bowl of a stand mixer fitted with the paddle attachment, or a large bowl with a hand mixer, place the butter, milk, and vanilla, and beat on medium speed until combined. Raise the speed to high and beat until creamy.
Add the salt, meringue powder, and about 3 1/2 cups of the confectioners’ sugar. Mix slowly until the sugar is incorporated.
Add up to the remaining 1/2 cup of the confectioners’ sugar, if necessary, to thicken the frosting.
Assemble the cookies
Transfer the filling to a pastry bag fitted with a 1/2-inch open piping top. When the cookies are cool, invert half of them and pipe about 1 1/2 tablespoons of filling onto the inverted cookies.
Top with the remaining cookies, right-side up, and push down gently to form a sandwich.