Preheat the oven to 350°F (175°C). Lightly grease a 9×13-inch baking pan or line it with parchment paper.
In a medium bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking powder, and salt until well combined.
In a large bowl, mix the melted unsalted butter and granulated sugar until smooth.
Add the eggs one at a time to the butter and sugar mixture, beating well after each addition.
Stir in the vanilla extract.
Fold the dry ingredients into the wet ingredients until just combined.
Gently fold in the shredded zucchini and semisweet chocolate chips until evenly distributed.
Pour the batter into the prepared baking pan and spread it evenly.
Bake in the preheated oven for 28 to 30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Remove from the oven and let the brownies cool completely in the pan on a wire rack before cutting into 16 squares.