In a medium bowl, sift together the flour, cocoa powder, salt and baking powder. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or with a handheld mixer in a large bowl, mix together the butter and sugar on medium-high speed until light and fluffy (about 3 minutes).
Add the egg and vanilla and mix on low speed until well combined.
Gradually add the dry ingredients to the wet ingredients and mix until a soft dough forms. Do not overmix.
Remove the dough and use hands to press the dough into a flat disc. Dough should be about ½ inch thick. Place on a cookie sheet lined with parchment paper and refrigerate for one hour.
Preheat oven to 350°F before removing the dough from the refrigerator.
Once the dough is chilled, remove from the cookie sheet. Dust the workspace with powdered sugar and roll dough to ¼ inch thick.
Using a round cookie cutter in the size of your choice, cut circles in the dough and place the cookies on a parchment paper lined cookie sheet about one inch apart.
Bake cookies for 12 minutes. Tops of cookies should be set, but soft to the touch. Remove from the oven and cool cookies on cookie sheet for 10 minutes. Remove and place on wire rack to fully cool.
Before assembling the ice cream sandwiches, freeze cookies for at least 30 minutes.
Using a large ice cream scoop, place one scoop of slightly softened coffee ice cream on one chocolate cookie. Top with another cookie and gently smoosh together. Repeat wtih remaining cookies (you may not get 16 sandwiches if you used a larger cookie cutter).
For best results, refreeze assembled cookie sandwiches for one hour to set. Enjoy!