Cream together the egg, butter, heavy cream, and Irish cream. Sift flour, cocoa powder, and powdered sugar and incorporate until a soft dough forms. Divide the dough into two disks, wrap tightly in plastic wrap, and refrigerate for at least 1 hour.

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper. Set aside.

Roll the chilled dough on a lightly floured surface to about ⅛ inch (3 mm) thickness.

Cut half of the cookies as solid rounds. From the remaining half, cut out the centers using a tiny shamrock-shaped cookie cutter. Place cookies on prepared trays, spacing slightly apart.

Bake for 8–10 minutes, until set but not overbaked. The cookies should feel firm around the edges. Cool completely on a wire rack before filling.

Let the ganache rest at room temperature for about 20 minutes, until it thickens and becomes spreadable but not fully set. Spread or pipe a small amount of ganache onto the solid cookies. Top with the shamrock-cut cookies, gently pressing to sandwich. Let the cookies set at room temperature or refrigerate briefly before serving. Enjoy!