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Preheat oven to 350°F. Grease and flour a 9″ by 13″ baking dish and set aside.
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Combine the oil, applesauce, sugar, and vanilla in a large bowl and mix well.
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In a separate bowl, whisk together the flour, cocoa powder, baking soda, and salt.
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Gradually mix the dry ingredients into the wet, stirring until completely combined.
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Fold in the shredded zucchini.
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Spread the batter evenly into the prepared baking pan and bake for 25-30 minutes, or until the top of the brownies springs back gently when touched.
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For the Frosting: Combine the cocoa powder and butter in a microwave safe bowl and microwave on high until melted. Pour the confectioners sugar into a separate bowl and blend with the milk and vanilla. Stir in the melted cocoa powder and butter mixture until smooth.
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Spread the frosting over the cooled brownies, cut into 12 pieces, and enjoy!