Preheat oven to 350 degrees. Spray a 9x13 inch baking dish with non-stick spray.
In a medium bowl, whisk together the flour, sugar, cocoa, baking soda, baking powder, salt and cinnamon.
Add the eggs, applesauce, oil, and vanilla to a small mixing bowl and whisk well to combine.
Pour the egg mixture over the dry ingredients and stir until just combined. Fold in the grated zucchini.
Spread mixture into the prepared baking dish. and bake for 50-60 minutes or until a tester comes out clean.
Cool completely before frosting. Let frosting set 15 minutes before cutting and serving.
Store cake in the refrigerator for up to 5 days or at room temperature for 2 days.You may use any type of chocolate frosting you like, but we love my mom's fudgy frosting. It pours the top of the cake like a dream and sets nice and smooth, but when you cut into the cake the frosting gets this gorgeous crackly top and tastes a bit like fudge.