Heat the oven to 350°F (175°C). Grease an 8-by-8-inch baking pan or line it with parchment paper, leaving a couple inches of overhang on two opposite sides to make lifting the brownies easy.

Grate the zucchini on the fine holes of a box grater. Wrap the shreds in a clean kitchen towel or several paper towels and squeeze firmly to remove as much liquid as possible. Do not skip this step, watery zucchini will make the brownies soggy.

In a large mixing bowl, whisk the melted coconut oil (or butter), sugar, egg, and vanilla until the mixture looks smooth and glossy. Stir in the squeezed zucchini until it is evenly distributed throughout the wet mixture.

In a separate medium bowl, whisk together the flour, dark cocoa powder, baking soda, and salt. Add the dry ingredients to the wet mixture and fold gently with a spatula until just barely combined. Fold in the dark chocolate chips.

Pour the batter into the prepared pan and smooth the top with a spatula. Sprinkle a few extra chocolate chips over the surface if desired. Bake for 25 to 30 minutes, until a toothpick inserted in the center comes out with only a few moist crumbs attached. Do not overbake if you want fudgy brownies.

Cool the brownies completely in the pan before slicing. This lets them set up properly and makes it easier to cut clean, neat squares.