1. Preheat the oven to 350°F. Spray a 9 by 13-inch baking pan with nonstick cooking spray.

For the Chocolate Zucchini Cake:

1. In a medium bowl, whisk together the dry ingredients: the flour, cocoa, baking soda, baking powder, and salt.
2. In the bowl of a stand mixer or in a large mixing bowl with a hand mixer, mix together the butter, oil, and sugar until combined, about 1 minute.
3. Add the eggs, one at time, beating for 20 seconds after each addition.
4. Mix in the buttermilk and vanilla until thoroughly combined.
5. On low speed, mix in the dry ingredients until combined.
6. Stir in the grated zucchini with a wooden spoon or spatula.
7. Pour into prepared pan and bake on the middle rack until a toothpick inserted into the center comes out clean, about 30 minutes.
8. Cool completely before frosting.

For the Chocolate Cream Cheese Frosting:

1. In the bowl of a stand mixer or in a mixing bowl with a hand mixer, beat the butter and cream cheese until smooth. Add the vanilla, cocoa, confectioners’ sugar, and pinch of salt. Beat until light and fluffy.
2. Spread on cooled cake.