Preheat the oven to 350°F. Coat a 9×13-inch baking dish with cooking spray.
Using a stand mixer fitted with the paddle attachment or a large bowl and hand mixer, beat the butter, sugar, egg, sour cream and vanilla on medium speed until creamy and smooth.
In a separate bowl, whisk together the flour, cocoa powder, baking soda and salt. Gradually add the dry ingredients to the butter mixture, mixing just until combined.
Gently fold in the shredded zucchini. Spread the thick batter evenly in the prepared baking dish.
Bake for approximately 30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs but no wet batter. Allow the brownies to cool completely.
Combine the peanut butter and chocolate chips in a microwave-safe bowl. Microwave in 30-second intervals, stirring thoroughly after each, until melted and smooth.
Spread the frosting evenly over the cooled brownies. Allow the topping to set slightly, then cut into 12 squares and serve.