Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking pan and line it with parchment paper, leaving an overhang on the sides for easy removal.
In a medium bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking powder, baking soda, and salt until well combined.
In a large bowl, whisk together the granulated sugar, light brown sugar, and vegetable oil until smooth.
Add the eggs one at a time to the sugar and oil mixture, whisking well after each addition.
Stir in the vanilla extract.
Fold the dry ingredients into the wet ingredients until just combined, being careful not to overmix.
Gently fold in the shredded zucchini and semi-sweet chocolate chips until evenly distributed.
Pour the batter into the prepared baking pan and spread it evenly with a spatula.
Bake for 28 to 32 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs but no wet batter.
Remove from the oven and allow the brownies to cool completely in the pan on a wire rack.
Once cooled, use the parchment paper overhang to lift the brownies out of the pan and transfer to a cutting board.
Cut into 12 squares and serve.