Prepare the Oven and Pan: Preheat the oven to 350°F (175°C). Line a 6-inch square baking pan with parchment paper, leaving a little overhang on the sides for easy removal.
Grate the Zucchini: Wash and finely grate the zucchini. If it is exceptionally watery, gently blot away some excess moisture with a paper towel. Do not squeeze it completely dry.
Mix the Dry Ingredients: In a mixing bowl, whisk together the all-purpose flour, cocoa powder, baking powder, and salt until evenly combined.
Combine the Wet Ingredients: In a separate bowl, whisk the egg, granulated sugar, brown sugar, vegetable oil, and vanilla extract until smooth. Stir in the grated zucchini.
Make the Brownie Batter: Add the dry ingredients to the wet mixture. Stir gently until no large streaks of flour remain. Fold in the chocolate chips without overmixing.
Fill the Baking Pan: Transfer the batter to the prepared pan. Spread it evenly into the corners with a spatula. Sprinkle a few extra chocolate chips on top if desired.
Bake the Brownies: Bake for approximately 25–30 minutes, checking for doneness toward the end of the baking time. A toothpick inserted into the center should come out with a few moist crumbs, not wet batter.
Cool and Serve: Let the brownies cool in the pan for approximately 30 minutes before lifting them out. Cut into four portions with a sharp knife and serve.