Preheat oven to 350 degrees and line 18 muffin cups with liners.
In a large bowl whisk eggs, both sugars, oil, and applesauce until smooth. Add in vanilla extract.
Add in melted chocolate, adding slowly if it is still hot, and whisking continuously.
In a medium bowl, combine flour, cocoa powder, salt, baking soda, and baking powder.
Add flour mixture to egg/sugar mixture and stir just until combined.
Stir in zucchini and chocolate chips.
Pour batter into muffin cups, filling just below tops of liners. Bake 20 to 25 minutes.