Shred the zucchini on large box grater. Transfer the shredded zucchini to a fine mesh strainer set over a bowl to drain while preparing the other ingredients. (SEE NOTES for helpful tips about preparing the zucchini)
Preheat oven to 350°F. Coat two 8.5x4-inch loaf pans with vegetable cooking spray. Set aside.
In a medium bowl whisk together the flour, cocoa, baking powder, salt and cinnamon. Set aside.
In a large mixing bowl whisk together the sugar, brown sugar, eggs, applesauce, espresso powder, and vanilla. Slowly drizzle the melted, cooled butter into the egg mixture and whisk until blended. Add the flour mixture, zucchini and chocolate to the bowl and gently fold together with a spatula until blended. The batter will be thick.
Divide the batter evenly between the two prepared pans. Bake for 50 - 55 minutes or until a skewer inserted in the center comes out clean, with no wet batter.
Cool for 30 minutes in the pan, then turn out onto a wire rack to cool. Warm bread is delicious but will crumble more than a cooled loaf. For best results, allow the loaf to cool completely before slicing with a serrated bread knife.