Preheat the oven to 350°F. Line a 9x13-inch baking pan with parchment paper, leaving some paper hanging on two sides. Set aside.
In a bowl, whisk together flour, cocoa powder, baking soda, baking powder, and salt. Set aside.
In a separate large mixing bowl, using a rubber spatula, mix together the sugar, vegetable oil, and vanilla extract until combined. Add the dry ingredients. Stir until all ingredients are incorporated. The mixture will be dry.
Stir in the zucchini, walnuts, and chocolate chips. The mixture will look dry, but keep stirring and the zucchini will release moisture.
Transfer the batter into the prepared baking pan. Spread evenly. Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean and dry.
Remove the zucchini brownies from the oven and let cool completely to room temperature on a cooling rack.
While the brownies are cooling, prepare the chocolate frosting. In a mixing bowl, whisk together the melted butter and cocoa powder until combined and shiny. Then, whisk in the powdered sugar, milk, and vanilla extract.
Spread the chocolate frosting immediately on top of the cooled brownies. Cut into 24 squares and serve!