Prep a 9x13" cake pan with parchment and spray with non-stick spray or rub with a light coat of oil or butter to prevent sticking. Set aside.
Combine dry ingredients. Set aside.
Grate the zucchini. Enough for 3 loosely packed cups. Set aside.
In a medium-large bowl, beat softened butter, oil, white sugar, and brown sugar. The mixture will lighten and whip up when it becomes fully incorporated.
Add eggs, one at a time, and beat after each addition. Add vanilla.
Add the dry ingredients in 2 batches. Mix on low speed just long enough to fully incorporate the flour. Avoid overmixing.
Switch to a spoon or spatula and fold in the zucchini. The batter will be thick but will be smooth & silky once the zucchini has a chance to meld with the rest of the ingredients.
Pour the batter into the prepared pan, spread evenly.
Bake at 350f for about 30 - 35 minutes or until a cake tester comes out clean. Avoid over-baking.