With a standing mixer or a hand mixer, beat butter until light and fluffy (about 1 minute).
Add in cocoa powder, sugar, baking powder, salt, and espresso powder. Mix until combined.
Next, add in melted and cooled semi sweet chocolate, and mix until combined.
Add in eggs, beating well after each addition.
Mix in 1 Tbsp of milk and vanilla extract.
Lastly, add in flour and mix until all the flour is incorporated. If the mixture is too dry and the dough is not coming together, add in the remaining Tbsp of milk.
Chill the dough for at least an hour.
Preheat oven to 375 degrees and line a large baking sheet with parchment paper (or spray with baking spray).
On a floured surface (you can also use cocoa powder or powdered sugar instead), roll dough out to 1/4” thick. Cut out shapes with cookie cutters and place them about 2” apart on the cookie tray.
Bake for 8-9 minutes, or until edges are just firm and the centers of the cookies are just set.
Allow to cool on the tray for a couple of minutes and then transfer to a cooling rack.
Once cooled, decorate as desired! Or, you can leave these cookies plain or dust with powdered sugar.