Prepare the pan and oven: Preheat your oven to 350°F (175°C). Line a 9x9-inch baking pan with parchment paper, leaving some overhang on the sides to make it easy to lift the bars out later. Lightly grease the paper if desired.
Grate and prep the zucchini: Grate the zucchini using the small side of a box grater. Place the grated zucchini in a clean kitchen towel or your hands and gently squeeze out some of the extra moisture. Do not squeeze it completely dry—leaving a bit of moisture keeps the bars soft and tender.
Mix the wet ingredients: In a large mixing bowl, whisk together the melted butter and brown sugar until smooth and glossy. Add the egg and vanilla extract, then whisk again until well combined and slightly thickened.
Combine the dry ingredients: In a separate bowl, stir together the flour, baking soda, baking powder, cinnamon, and salt. Make sure everything is evenly mixed so the leavening and spices are distributed throughout the batter.
Bring the batter together: Add the dry ingredients to the wet ingredients and gently stir with a spatula or spoon until just combined. The batter will be thick. Avoid overmixing to keep the bars soft and tender.
Fold in zucchini and chocolate chips: Gently fold the grated zucchini into the batter until evenly distributed. Then fold in the chocolate chips, reserving a small handful to sprinkle on top if you like. The batter will look thick and slightly speckled with zucchini and chocolate.
Spread the batter and bake: Pour the batter into the prepared baking pan and spread it into an even layer using a spatula. Sprinkle the reserved chocolate chips on top. Bake for 22–26 minutes, or until the top is set and a toothpick inserted into the center comes out mostly clean with just a few moist crumbs (not wet batter).
Cool, slice, and serve: Remove the pan from the oven and let the bars cool completely in the pan. Use the parchment overhang to lift the cooled bars out onto a cutting board. Slice into squares or rectangles and serve. Enjoy them slightly warm or at room temperature for the best soft, chocolatey texture.