Preheat oven to 350 F. Line a 9x13-inch baking pan with parchment paper and set aside.
In a large bowl, whisk together flour, cocoa powder, baking soda, baking powder and salt. Set aside.
In a separate large bowl, beat together C&H® Granulated Sugar Easy Baking Tub, C&H® Light Brown Sugar, vegetable oil, melted butter, sour cream and vanilla. Mix on medium-high speed until well combined, about 2 minutes. Add eggs and mix until combined, about 1 minute.
Pour wet ingredients into the bowl of dry ingredients. Use a rubber spatula to mix just until combined (avoid over mixing). Add shredded zucchini and chocolate chips. Stir just until incorporated.
Transfer batter to prepared pan and spread batter evenly. Bake at 350 F for 30 to 35 minutes or until a toothpick inserted in the center comes out with little to no crumbs. Allow cake to cool completely in the pan.
For the frosting, beat butter with an electric mixer until light and fluffy, about 2 minutes. Add C&H® Powdered Sugar and cocoa powder and mix until combined. Add vanilla and milk, one tablespoon at a time, and mix until frosting is smooth.
Transfer frosting to cooled cake and use an offset spatula to spread evenly. Cut cake and serve.