Line two rimmed baking sheets with parchment paper.
In a medium bowl, whisk together the flour, cocoa powders, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar on medium speed until light and fluffy, about 1 minute, scraping the bowl with a flexible spatula as needed.
Reduce the speed to low, add the egg and vanilla and continue to mix until combined, about 1 minute, scraping the bowl as needed.
Add the dry ingredients all at once and mix just until incorporated.
Use your hands or a flexible spatula to knead or stir the dough briefly. It will be quite sticky and this is ok. Divide the dough into quarters and place one quarter on a large sheet of parchment paper.
Place another large sheet of parchment on top of the dough and roll it out until it is about 1/4-inch (6-mm) thick. Have ready a small bowl of cocoa for dipping your cookie cutter.
Remove the top layer of parchment and begin pressing a 2-inch (5-cm) cookie cutter into the rectangle of dough, dipping the cutter in cocoa powder each time you do so. Once the rectangle is covered in circles, place it on a baking sheet, still on its sheet of parchment, and place into the freezer. Chill for 20 minutes.
Take the rectangle of dough from the freezer and begin removing the wafers. You will have to peel away the parchment from underneath each one. Place the wafers on the prepared baking sheets. The wafers don’t spread very much so they can be placed pretty close to one another, about 24 wafers per tray. Collect the scraps and set aside.
Repeat the cutting and chilling process with the remaining dough quarters and any scraps.
Once all of the wafers have been placed on baking sheets, freeze for 20 minutes.
While the wafers are chilling, preheat the oven to 350°F (177°C).
Bake one tray at a time until flattened and beginning to crisp, about 15 minutes, rotating at the halfway point. Let the wafers cool before filling them.