Preheat the oven to 350 degrees F and coat a 9×13 baking dish with cooking spray. Using a stand mixer fitted with the paddle attachment (or a large mixing bowl with a hand mixer), combine the butter, sugar, egg, sour cream and vanilla extract and beat on medium speed until creamy and free of lumps.
In a separate bowl, combine the flour, cocoa powder, baking soda and salt. Mix well. Gradually add to the butter-sugar mixture and beat on medium speed until just combined. Fold in the shredded zucchini.
Pour the batter into the prepared baking dish and spread evenly. Bake in the preheated oven for 30 minutes, or until a toothpick inserted into the center comes out clean. Let cool.
In a small microwave-safe bowl, combine the peanut butter and chocolate chips. Heat in 30-second intervals, stirring after each, until mixture is creamy and free of lumps. Spread evenly over the cooled brownies, cut into squares and serve!