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Preheat oven to 350°F/180°C. Grease an 8×8-inch pan.
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In a large bowl, whisk together flour, cocoa powder, baking powder, baking soda, cinnamon, and salt. Set aside.
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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 ½ cup chocolate chips.
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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.
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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).