Preheat oven to 350F. Grease a 9x13" pan.
In a small bowl, mix together the milk and vinegar and let sit to thicken.
Make the cake: In a medium size bowl, cream together the butter and oil.
Add the sugar, and eggs one at a time. Then add the vanilla and milk mixture.
In a separate bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and cinnamon.
Pour the dry ingredients into the wet ingredients and mix until completely combined. Then fold in the shredded zucchini and chocolate chips. Batter will be slightly thick.
Pour batter into a 9x13" pan. Bake for 33-36 minutes or until the cake is baked through. To test for doneness, insert a toothpick into the center of the cake. If it comes out clean, it is done. Allow to cool completely in the pan set on a wire rack. The cake must be completely cool before frosting and assembling.
Make the frosting: In a medium size bowl, cream the cream cheese and butter together using an electric mixer. Add the vanilla and icing sugar and continue blending.
Cover the leftover cake and store at room temperature for 2-3 days or in the refrigerator for up to 5 days.