Preheat oven 350℉ and thoroughly grease or spray the inside of a 6 inch round pan. Line the bottom of the pan with parchment paper to ease removal from the pan.
In a small bowl, add flour, cocoa powder, baking soda, salt, baking powder and espresso powder, if using, and stir until combined.
In a medium bowl, whisk together sugar, buttermilk, egg and vanilla until smooth. Add the dry ingredients and stir until combined.
Stir in the shredded zucchini until combined.
Pour into prepared pan and bake for 35 minutes, until a toothpick inserted in the center comes out clean. The cake should spring back when touched.
Allow to cool for 15-20 minutes. Once cooled, invert onto a plate and remove parchment paper. Frost cake once completely cooled.
Frosting:
Whip together softened cream cheese and butter. Add cocoa powder, vanilla, and powdered sugar and whip until thoroughly mixed.