In a medium sized mixing bowl, combine the flour, cocoa powder, and baking powder. Set this aside for now.
In a stand mixer with the paddle attachment, cream together the cup of cold, salted butter with the granulated sugar.
Add in the egg, teaspoon of vanilla extract, peppermint extract, and tablespoon of espresso powder. Mix until just combined.
To the stand mixer bowl, slowly add in the dry ingredients from the medium sized mixing bowl. Mix on low until the dough comes together and forms a ball. It will be dry at first but it will come together.
Lay out a piece of parchment paper on the counter. Roll the dough out onto the parchment paper to 3/8" thick. Cut out the cookies and bake on a lined cookie sheet for 7-10 minutes or until the cookies no longer look wet. Allow the cookies to cool on the baking sheet for at least five minutes before removing them.