Preheat oven to 350°F (175°C). Grease a 9" x 5" loaf pan. If you like, line the pan with parchment paper and grease the paper.
Whisk together the flour, brown sugar, sugar, cocoa powder, baking soda, cinnamon, salt, and baking powder. Make a well in the center.
In a separate bowl, combine the butter, eggs, milk, and vanilla.
Add the butter mixture to the well in the flour mixture. Stir just until combined or a few streaks of flour remain.
Stir in the zucchini, chocolate chips, and nuts (if using), mixing just until combined.
Transfer the batter to the prepared pan, and spread evenly. Bake 60 to 70 minutes, or until a pick inserted into the center comes out clean.
Cool in the pan on a wire rack for 10 minutes. Then remove the bread from the pan and place directly on a wire rack to cool completely.
Notes
*This measurement doesn't have to be especially accurate. Somewhere between 120g and 150g should be fine. Place a paper towel on top of the grated zucchini to absorb some of the water before mixing.
Store in an airtight container at room temperature up to 3 days.