To make the cake:
Preheat oven to 350 degrees F.
Grease 9x13" baking dish with cooking spray and set aside.
In large bowl with electric mixer, beat together vegetable oil, coconut oil, sugar, vanilla, baking soda, baking powder, and salt until well combined.
Add eggs and beat until combined.
Alternate adding yogurt and flour, in 3 additions.
Add cocoa powder and beat until combined.
Fold in zucchini.
Pour into prepared baking dish.
Bake in preheated oven for 33-38 minutes, until toothpick comes out of the middle clean.
Let cool completely.
To make the frosting:
Beat butter on high until light and fluffy, about 2 minutes.
Add powdered sugar and cocoa until combined.
Add yogurt, salt, and vanilla, until well combined.
Once cake is cool, frost the cake.
Cut into squares and enjoy!
Store in refrigerator up to 5 days.