Preheat oven to 350 and grease a 12x17 (or similar) jelly roll pan.
In a medium bowl whisk together flour, baking soda, cinnamon, and salt.
In a large bowl cream together zucchini, sugars, eggs, vanilla, and greek yogurt.
Add dry ingredients to wet ingredients and mix until combined. Spread batter in prepared pan.
Bake for 20-25 minutes until cake springs back when gently pressed with a finger. Allow to cool.
For the frosting, cream together butter, powdered sugar, cream cheese, vanilla, and milk until smooth. Spread over cooled cake.