Preheat the oven to 350F.
Cream together the butter and the sugars in a mixing bowl until well combined.
Add the vanilla extract, add the eggs one by one, and add the espresso, mixing until just combined in between each addition.
In a separate bowl, whisk together the flour, cocoa powder, and baking soda.
Add the dry ingredients to the butter and egg mixture and mix until combined.
Add the chocolate chips and mix until combined.
On a baking sheet with waxed paper or a silicone mat, spread the batter into a rectangle of about 4-6 inches in width and about ¾-inch thickness.
Bake the batter at 350F for 30-35 minutes until the cookie becomes firm and the top springs back when pressed lightly with a finger.
Allow the cookie to cool for at least 60-90 minutes before cutting the large cookie into thin slices of about ½-inch width.
Preheat the oven to 325F.
Place the slices onto the baking sheet with one of the sliced sides facing upwards. Bake at 325F for 15 minutes. The biscotti should be firm and slightly dry.