Preheat oven to 350°F (180°C). Spray a 9-inch round cake pan with baking spray with flour. Line bottom of pan with parchment paper.

In a medium bowl, whisk together flour, salt, baking soda, cinnamon, and baking powder.

In a large bowl, whisk together granulated sugar, oil, brown sugar, eggs, and vanilla until well combined; whisk in zucchini. Gradually stir in flour mixture just until dry ingredients are moistened. Stir in chocolate until mixture is well combined. Spread batter into prepared pan. Tap pan on a kitchen towel-lined counter a few times to spread batter.

Bake until a wooden pick inserted in center comes out clean, 50 minutes to 1 hour. Let cool in pan for 10 minutes. Remove from pan, and let cool completely on a wire rack.

Spread Whipped Cream Cheese Frosting onto cooled cake. Cover and refrigerate for up to 3 days.