Preheat oven to 350°F. Grease a 9x5-inch loaf pan and line with parchment paper, leaving overhang on the long sides.
Grate zucchini using the large holes of a box grater. Toss with 1/2 teaspoon salt in a colander and let sit 10 minutes. Transfer to a clean kitchen towel, gather the corners, and wring out over the sink until barely any liquid comes out.
In a medium bowl, whisk together flour, cocoa powder, baking soda, baking powder, cinnamon, nutmeg, and a pinch of salt.
In a large bowl, whisk together oil, 1 cup sugar, eggs, and vanilla until smooth and slightly lightened, about 1 minute.
Add dry mixture to wet mixture and fold with a rubber spatula until just combined. Do not overmix.
Fold in the squeezed zucchini and chocolate chips until evenly distributed. Batter will be thick and slightly shaggy.
Scrape batter into prepared pan and spread even. Sprinkle remaining 2 tablespoons sugar evenly over the top.
Bake for 45-50 minutes, until a toothpick inserted in the center comes out with a few moist crumbs (not wet batter). If top browns too quickly, tent with foil at 30 minutes.
Cool in pan 15 minutes, then lift out using parchment and transfer to a wire rack to cool completely before slicing – at least 30 minutes.