Preheat oven to 350°F. Lightly grease and flour a 9x13-inch baking dish. Set aside.

In a medium bowl, whisk together the flour, baking soda and cinnamon. Set aside.

In the bowl of an electric mixer, beat together the melted butter, oil and sugar until smooth. Add the eggs and vanilla and beat until well combined. Stir in the combined dry ingredients and mix well. Slowly beat in the buttermilk. Fold in the shredded zucchini.

Spread the batter evenly into the prepared baking dish. Bake for 35-40 minutes or until a toothpick inserted in the center comes out clean. Let cool completely on a wire rack.

For the frosting, beat the cream cheese and butter in the bowl of an electric mixer until smooth. Add the vanilla and cinnamon and beat until well combined. Add the powdered sugar, 1 cup at a time, until well combined and frosting is thick yet spreadable. Add a tablespoon or two of milk if the frosting needs to be thinner for spreading over the cake.

Spread the frosting evenly over the cooled cake.