Preheat oven to 350°F. Grease and flour a 9x13-inch rectangular cake pan.
You can also use nonstick baking spray (the kind with flour).
Whisk salt, baking powder, baking soda, cinnamon, and flour in a medium bowl. Set aside.
Whisk eggs until beaten, then whisk in oil, vanilla and both sugars. Whisk until combined, then add dry ingredients and stir with a sugars. Whisk until combined, then add dry ingredients and stir until moistened. Stir in zucchini.
Place batter in prepared pan. Bake for 40-45 minutes or until a toothpick comes out clean in the center.
Let the cake completely cool before removing from the pan and frosting.
To make the frosting: beat cream cheese and butter until smooth. Add powdered sugar, 1 cup at a time, until the mixture comes together, then add vanilla and salt. Beat until smooth.
Frost the top of the cake with the frosting.
Store loosely covered in the refrigerator for up to 3 days.