Prepare the oven and pan. Preheat the oven to 350°F (175°C). Grease a 9-by-5-inch loaf pan or line it with parchment paper for easier removal.
Combine the dry ingredients. Whisk together the flour, baking powder, baking soda, salt, and cinnamon in a medium bowl.
Mix the wet ingredients. In a separate large bowl, whisk the eggs, vegetable oil, brown sugar, granulated sugar, and vanilla until smooth.
Add the zucchini. Stir the shredded zucchini into the wet mixture until evenly distributed.
Combine the batter. Add the dry ingredients to the wet ingredients. Fold gently just until no large streaks of dry flour remain. Stir in chocolate chips or nuts, if using.
Fill the loaf pan. Transfer the batter to the prepared pan and smooth the top. Sprinkle with coarse sugar.
Bake. Bake for 55 to 60 minutes, or until a toothpick inserted near the center comes out with a few moist crumbs but no raw batter.
Cool. Let the bread rest in the pan for about 10 minutes. Transfer it to a wire rack and allow it to cool before slicing.