In a large bowl, use an electric mixer to combine the sugar and butter until light and fluffy. Gradually beat in the cocoa powder, baking powder and espresso powder. Beat for a minute or so, then beat in the eggs one at a time. Stir in the flour. Then stir in the chocolate chunks. Cover the dough and chill for about 20 minutes.
Preheat the oven to 375℉. Line a baking sheet with parchment paper.
Divide the dough into 2 equal parts. Roll each into a 9-inch log. Place the logs on the prepared baking sheet, about 4-inches apart. Flatten slightly.
Bake for 20 to 25 minutes, until a toothpick inserted into the center comes out clean. Cool for 5 minutes, and then transfer to a wire rack to let cool for 1 hour.
Preheat the oven to 325℉. Cut each log into ½-inch wide diagonal slices. Place the slices on a parchment-lined baking sheet.
Bake for 9 minutes. Turn the biscotti over and bake for an additional 7 to 9 minutes. Cool completely. Set the biscotti on a wire rack set over wax paper.
ADD THE ICING:
In a microwave-safe bowl, microwave the chocolate chunks and shortening until melted and smooth. Drizzle the chocolate haphazardly over the cooled biscotti. Let the chocolate set completely before storing. Store in a sealed container with waxed paper in between layers.