The dough needs at least a few hours in the fridge, plan accordingly. It can also be left overnight.
Set the butter, sugar, salt and vanilla in the bowl of a stand mixer (or use a hand mixer) and affix the paddle attachment. Beat until light and airy, for at least a few minutes.
Add in the egg whites and mix well to combine. Sift in the black cocoa, baking soda, and flour and beat until the dough is smooth and has no visible unmixed flour.
Wrap the dough into a sheet of plastic wrap and roll into a disk shape. Chill in the fridge for four hours or overnight.
Prepare two cookie sheets with parchment paper (some butter/grease on the pan will help hold the parchment down).
Roll out the dough to about half an inch thickness, and use a one inch cookie cutter to cut out shapes. Place the cookies on the prepared sheets, leaving a bit of space between them so they won’t stick together when they bake. Reroll the dough (flouring as needed) to punch out all of it into small cookies.
Set the trays in the fridge to chill for 10 minutes and preheat the oven to 325 F. Bake the cookies until matte all over, for about 10-12 minutes. Let cool completely.
Make the icing: set two egg white in the bowl of a stand mixer (you can also use a hand mixer) and use the whisk attachment to whisk until frothy (even at the bottom of the bowl). Add the sifted powdered sugar in spoonfuls, slowly. If some gets caught at the edges of the bowl stop and scrape it down. Once all the sugar is in, add the salt and vanilla. Keep whisking/mixing until the icing is stiff and thick. Transfer to a piping bag fitted with a star shaped piping tip and carefully pipe a rosette on top of each cookie.
You can leave the cookies on the tray so the topping dries out fully or set them in an oven preheated to 150 F for 20-30 minutes to dry.