Heat the oven to 350 degrees F and place a rack in the center, then spray an 8.5 x 4.5 x 2.75-inch loaf pan and line it with parchment paper. The parchment should hang over the sides a bit so the baked loaf lifts out easily later.
Check the grated zucchini and, if it seems especially wet, press it gently between paper towels before using. You want the zucchini moist but not dripping, since too much surface water can weigh down the batter.
Combine the zucchini, brown sugar, granulated sugar, eggs, olive oil, and vanilla in a medium bowl. The mixture will look glossy, loose, and slightly chunky from the zucchini strands.
Whisk the flour, Dutch process cocoa powder, salt, baking soda, and baking powder in a separate large bowl. This helps spread the leavening and cocoa evenly so the loaf rises and colors more consistently.
Add the wet mixture to the dry mixture and stir just until no dry pockets remain, then fold in most of the chocolate chips and reserve 2 tablespoons for the top. The batter will be thick and heavy, and that dense texture is exactly what you want for a fudgy loaf.
Scrape the batter into the prepared pan and scatter the reserved chocolate chips over the surface. The top will look full and textured, which helps create a craggy finish as it bakes.
Bake for 45 to 50 minutes, then cool the bread in the pan for 5 minutes before transferring it to a wire rack to cool further. A tester inserted in the center should come out without wet batter, though a little melted chocolate on it is normal.