Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a mixing bowl, sift together the flour, cocoa powder, baking soda, and salt. Set aside.
In another bowl, using an electric mixer, cream the softened butter and granulated sugar until light and fluffy.
Add the egg, vanilla extract, and cooled espresso to the butter mixture. Mix until well combined.
Gradually add the dry ingredient mixture to the wet ingredients, mixing until just combined. Do not overmix.
Using a tablespoon or cookie scoop, drop rounded balls of dough onto the prepared baking sheet, leaving space between each cookie.
Bake in the preheated oven for 10 minutes, or until the cookies are set and the edges are just firm.
Remove from the oven and let the cookies cool on the baking sheet for a few minutes before transferring them to a cooling rack.
Once cooled, dust the cookies with powdered sugar for a finishing touch.
For a stronger coffee flavor, consider adding additional espresso or replacing some of the granulated sugar with instant coffee granules in the dough.