Preheat the oven to 350°F. Coat two 8×4-inch loaf pans with butter or cooking spray.
Shred the zucchini and transfer it to a fine-mesh sieve or colander. Allow it to drain for several minutes, then gently press it with the back of a spoon to remove additional liquid. Removing excess moisture helps prevent an overly wet loaf and promotes more even baking.
Place the sugar, room-temperature eggs, vanilla extract, slightly cooled melted butter, and kosher salt in a large mixing bowl. Whisk for approximately 1–2 minutes, or until thoroughly blended and somewhat lighter in appearance. Ensure the butter has cooled enough that it will not cook the eggs.
Add the all-purpose flour, baking soda, and cinnamon to the wet mixture. Fold gently with a whisk or wooden spoon just until the visible streaks of flour disappear. Avoid excessive mixing, which can strengthen the gluten and produce a firmer, tougher texture.
Fold the drained shredded zucchini into the batter with a spatula or wooden spoon, using gentle sweeping motions until evenly dispersed. Add the chocolate chips and fold only until they are distributed throughout the mixture. The finished batter should appear thick and textured.
Divide the batter equally between the two prepared loaf pans. Lightly smooth the surfaces with a spatula.
Bake at 350°F for 40–60 minutes. The loaves are ready when the tops are golden brown and a toothpick inserted into the center emerges mostly clean with only a few moist crumbs. Melted chocolate on the tester is acceptable, but there should be no uncooked batter. A tester inserted closer to the edge should come out clean.
Remove the pans from the oven and allow the loaves to cool in them for 10 minutes so their structure can firm sufficiently for removal.
Turn the loaves out onto a wire cooling rack and leave them until completely cooled before slicing. Full cooling helps the bread hold together and allows cleaner, less crumbly slices.