Preheat your oven to 350°F (177°C). Grease a 9×5-inch loaf pan or an 8×4-inch pan for a taller loaf.
In a large mixing bowl, whisk together the flour, cocoa powder, baking soda, baking powder, salt, and espresso powder. Toss the chocolate chips into this dry mixture.
In a separate medium bowl, whisk the eggs, oil, Greek yogurt, sugar, and vanilla until smooth and thoroughly combined.
Pour the wet mixture into the bowl of dry ingredients. Stir gently until just combined—be careful not to overmix! Fold in the shredded zucchini.
Transfer the thick batter into the prepared loaf pan, spreading it evenly. Bake for 45-55 minutes, loosely covering the pan with foil halfway through baking to prevent the top from overcooking. The bread is done when a toothpick inserted in the center comes out with only moist crumbs.
Cool the bread in the pan on a wire rack for 1 hour. Optionally, press a few extra chocolate chips onto the warm top for a polished presentation.
After cooling, remove the loaf from the pan, and allow it to cool completely on the rack. Enjoy now or store for later!