Preheat the oven to 350°F (175°C) and line 18 muffin cups with paper liners.
In a large bowl whisk together the eggs, white sugar, brown sugar, vegetable oil, and applesauce until smooth, then stir in the vanilla extract.
In a small saucepan over low heat, gently melt the chopped dark chocolate, stirring frequently; add it slowly to the egg mixture while whisking so the hot chocolate incorporates smoothly.
In a medium bowl combine the all-purpose flour, dark cocoa powder, salt, baking soda, and baking powder.
Add the dry ingredients to the wet ingredients and stir just until combined; do not overmix.
Fold in the grated zucchini and dark chocolate chips until evenly distributed.
Spoon the batter into the prepared muffin cups, filling each just below the top of the liner.
Bake for 20 to 25 minutes, until a toothpick inserted into the center comes out with a few moist crumbs.
Let the muffins cool in the pan for a few minutes, then transfer to a wire rack to cool further.