In a small bowl, combine flour, cocoa powder, cinnamon, baking powder, baking soda, and salt and mix well.
In a separate, and larger mixing bowl, add sugar, egg, oil, and vanilla and mix well. Stir in yogurt.
Add dry flour mixture and stir well.
Fold in Zucchini.
Pour batter into prepared pan and smooth with the back of a spoon so it's even in the pan.
Bake for 20 minutes or until a toothpick inserted in the center comes out clean.
Let cool completely before frosting and cutting into 9 squares.