Preheat the oven to 350°F (175°C).
Line a 9 × 9-inch baking pan with parchment paper, leaving overhang on two sides.
Wash and finely grate the zucchini.
Place the shredded zucchini in a clean kitchen towel and gently squeeze out only the obvious excess moisture.
In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt.
In a large mixing bowl, whisk together the melted butter, vegetable oil, brown sugar, and granulated sugar until smooth.
Add the eggs one at a time and whisk until incorporated.
Stir in the vanilla extract.
Add the dry ingredients to the wet mixture and fold gently.
Fold in the shredded zucchini until evenly distributed.
Fold in 3/4 cup of the chocolate chips.
Transfer the batter to the prepared baking pan and spread gently toward the corners.
Sprinkle the remaining 1/4 cup chocolate chips over the top.
Bake for 28–34 minutes, until the edges are set and a toothpick inserted into the center comes out with moist brownie crumbs but no liquid batter.
Cool completely in the pan.
For cleaner slices, refrigerate for approximately 30 minutes after cooling.
Lift the brownies from the pan using the parchment paper.
Cut into 16 squares and serve.