Preheat oven to 350°F (175°C) and grease a 9x5 inch loaf pan.
In a medium bowl, whisk together flour, dark cocoa powder, baking soda, baking powder, and salt.
In a large bowl, beat the eggs, granulated sugar, brown sugar, oil, and vanilla extract until well combined.
Gradually fold the dry ingredients into the wet ingredients until just combined.
Fold in the grated zucchini and 0.75 cups of the white chocolate chips.
Pour the batter into the prepared loaf pan and sprinkle the remaining 0.25 cups of white chocolate chips on top.
Bake for 55 to 65 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.