1. Preheat oven to 350°F. Line an 8 by 8-inch metal baking pan with parchment paper and spray with nonstick cooking spray.
2. In a large bowl, whisk together the flour, cocoa, sugar, salt, and baking soda.
3. In a small bowl, whisk together the melted butter, oil, sour cream, eggs, egg yolk, and vanilla extract.
4. Make a well in the center of the dry ingredients and pour in the wet ingredients. Stir until a few streaks of flour remain.
5. Squeeze out any additional moisture from the shredded zucchini before adding to the batter. Add the zucchini and chocolate chips. Stir until just barely combined.
6. Pour the batter into the prepared pan and bake for 30 minutes, or until a toothpick or cake tester comes out clean. If your cake sinks slightly in the middle, that's normal because it’s so moist and rich!
7. Let cool completely.
8. In a medium bowl, stir together the powdered sugar and milk with a fork until smooth and thick but pourable. Drizzle all over the cooled cake. Let set before serving.