Preheat the oven to 350°F/175°C. Line and grease a square 8-inch or round 9-inch metal baking pan.
In a large bowl, add 1/2 cup warm water, 1/2 cup sour cream, 1/4 cup oil, 1 egg, 1 tsp vanilla, and 1 tsp instant espresso (optional). Whisk together until combined.
In a separate, medium-sized bowl, whisk together 1 cup + 2 Tbsp flour, 1 cup sugar, 1/3 cup cocoa powder, 1 tsp baking powder, 3/4 tsp baking soda, and 1/2 tsp salt.
Add the dry ingredients to the wet ingredients and mix until just combined. Then fold in 1 1/2 cups of peeled and shredded zucchini that's been blotted/gently dried with a paper towel and 2/3 cup of chocolate chips into the batter (I like to use mini chocolate chips, but any type works!). The goal of blotting the zucchini is to remove just a bit of the moisture, but not all of it! You do not want to wring out the zucchini.
Pour the batter into the prepared pan, then sprinkle the remaining 1/3 cup of chocolate chips on top of the batter. Bake for 35-40 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs. Remove the pan from the oven.
Place the pan on a wire cooling rack and let the cake cool fully in the pan. If you're in a rush, place the whole pan in the freezer for 30 minutes to accelerate the cooling process. This cake can be stored at room temperature for up to 3 days or in the fridge for 5 days.