Preheat your oven to 350 degrees F. Spray a jelly roll pan with non-stick cooking spray. Set aside.
In a medium mixing bowl, stir the flour, baking powder, baking soda, salt, and cinnamon. Set aside.
In a large mixing bowl, beat together the sugar, oil, and eggs. Add the flour mixture to the sugar mixture and mix on medium speed. Then, slowly add milk while the mixer is running. Use a rubber spatula to fold the zucchini into the cake batter until well combined. Pour the batter into the prepared pan.
Bake for 18-20 minutes. Remove from the oven and rest on a wire rack.
Frosting
Add the butter to a microwave-safe bowl. Cover the bowl with a plate (to prevent splatters) and microwave for 1 minute. Remove the plate and stir in the vanilla and buttermilk. Place the bowl back in the microwave, uncovered, and heat for 2 minutes, stirring every 30 seconds.
Take the bowl out of the microwave and stir in the cocoa powder and powdered sugar until well combined. Return the bowl to the microwave and heat for 1 minute, stirring halfway through the cooking time. If needed, heat for an additional 30 seconds until frosting is smooth and there are no clumps.
Pour the frosting over the cake and spread evenly over the top. Let the frosting cool and harden. Cut into 20 slices (5x4 grid) and serve.
Notes
I like the tang that the buttermilk adds to the frosting, but you can substitute whole milk or half-and-half if you prefer.