In the bowl of a stand mixer, beat your butter until smooth. Add the sugar and continue beating until creamy. Add the eggs, espresso powder, and vanilla extract, mixing until combined. A half cup at a time, add your baking cocoa and flour, mixing between each new addition until just combined. Wrap your dough in plastic wrap and allow to cool in the refrigerator for about an hour.
Preheat your oven to 350F/175C and line your baking sheets with parchment paper. Roll out your dough to about 1/2″ thick, and cut out your cookies. You can really make them as big or small as you want, just be sure to adjust your baking time accordingly (mine are 3″ across). Bake your cutouts for 6-10 minutes (depending on size) until no longer shiny on top.
Once the cookies have cooled completely, fill them with your peppermint ice cream. If you want nice, neat circles of ice cream, melt your ice cream and spread it evenly in a plastic wrap lined 9″x13″ dish. Using the same cookie cutter you used to cut out your cookies, cut out your ice cream. Sandwich the ice cream between two cookies, and dip in melted chocolate if you’d like. Garnish with crushed peppermint.