Preheat oven to 350°F/180°C. Grease an 8×8-inch pan.
In a large bowl, whisk together flour, cocoa powder, baking powder, baking soda, cinnamon, and salt. Set aside.
In another medium bowl, whisk eggs and sugar until well combined. Add oil, sour cream (or yogurt/buttermilk), and vanilla extract, and whisk until combined. Add egg mixture into flour mixture and fold with a rubber spatula just until combined. Do not overmix. Fold in grated zucchini and 1/2 cup chocolate chips.
Scrape batter into prepared pan and smooth the top. Sprinkle the top with chocolate chips if desired. Bake for 35-40 minutes or until a toothpick inserted into the center of the cake comes out clean. Allow cake to cool completely on a wire rack.
Cake can be kept in the refrigerator in an airtight container for up to 5 days or in the freezer for up to 2 month (thaw overnight in the fridge).