Preheat the oven to 350°F. Grease a 10 cup bundt pan generously and set aside.
Grate the zucchinis and place on several layers of paper towels to absorb excess moisture. Use a towel and gently press the zucchini to release the moisture. You don't want it completely dry, just slightly less wet. I ended up with a couple of cups of grated zucchini but it honestly doesn't affect the recipe if you have more or less. I would say between 2 and 3 cups is perfect.
Whisk granulated sugar, eggs, applesauce, butter, and vanilla extract together in a large mixing bowl.
Whisk the flour, baking soda, salt, cinnamon and cocoa powder together. Reserve a couple tablespoons of the mixture, set aside.
Stir the flour mixture into the wet mixture just until combined.
Combine the chocolate chips with the reserved flour mixture. Add chocolate chips and grated zucchini to the batter and stir just until all ingredients are combined.
Pour the batter into the prepared bundt pan. Bake the cake for 55 to 65 minutes or until an inserted toothpick comes out with a few moist crumbs. Let the cake cool for ten minutes before inverting onto a plate. Let cake cool completely.