Cream together butter, granulated sugar, and brown sugar using an electric mixer until light and fluffy (2-3 minutes). Add egg and Baileys, mixing until combined. Gradually incorporate cocoa powder and espresso powder until smooth.

Cover the bowl with plastic wrap and refrigerate for at least 30 minutes. Preheat oven to 350°F (175°C) during this time.

Line a baking sheet with parchment paper. Scoop rounded portions of dough onto the sheet, leaving space between each ball. Bake for 10-12 minutes, until edges are set and centers look slightly soft.

Remove cookies from oven and let sit on baking sheet for 5 minutes before transferring to wire rack to cool completely.

Whisk together powdered sugar and Baileys until smooth to prepare glaze. Adjust consistency by adding more sugar or Baileys.

Once cookies are cool, dip the tops into the glaze, allowing excess to drip off. Place back on wire rack and let icing set before serving.