Sift the flour, cocoa powder, and baking powder into a medium-sized bowl, whisk together to combine, and set aside.
Beat butter in the bowl of a stand mixer (or a large bowl if using a hand mixer) until smooth. Add the sugar and beat until light and fluffy on medium-low speed. Then mix in the salt and mint extract. Next, add the dry ingredients in 2 additions and mix until just incorporated. Do not overmix. The dough will be crumbly, but it will come together when chilled.
Place the dough on a piece of plastic wrap and gently knead the dough into a disc. Then, set the dough in the fridge and chill for at least 1 hour (or until firm enough to cut with cookie cutters).
Preheat the oven to 325°F.
Roll out the dough between two sheets of plastic wrap until it’s an ⅛-inch thick. Use a cookie cutter to cut out round cookies from the dough. If the dough gets soft while working with it, put it back in the freezer for a few minutes until it firms back up. Place the cookies on a cookie sheet and bake for 13 minutes. Rotate the pan halfway through baking to ensure even baking.
Set the cookie sheet on a wire rack to cool for 5-10 minutes and then transfer the cookies to the wire rack to cool completely.