Preheat the oven to 350 degrees. Line an 8 x 8 baking dish with some parchment paper then spray with cooking spray.
Make the brownies by combining the oil, chocolate chips and cocoa powder in a saucepan over medium-low heat. Whisk or stir often, until the chips are melted and the mixture is smooth.
Remove pan from the heat and whisk in the sugar until combined.
Add the whole egg and additional egg yolk, one at a time, whisking in between each addition.
Add the vanilla extract and whisk until smooth and creamy.
Add the squeezed out shredded zucchini and mix until well combined.
Combine the flour, salt and baking soda in a bowl; mix well.
Gradually add the flour mixture to the zucchini mixture until combined. Be careful not to over mix.
Spread batter evenly into the prepared baking dish and bake for 27-30 minutes, or until a wooden tester inserted in the center comes out clean or with only a few moist crumbs.
Make the frosting while the brownies are baking by combining the butter, chocolate chips, milk and cocoa powder together in a small saucepan over low heat.
Cook, stirring often, until the chocolate chips melt then immediately remove from the heat. Side Note: Don't overcook the chocolate or it will seize and not be spreadable.
Whisk in the vanilla and the powdered sugar, until combined and smooth. It will be thick.
When the brownies come out of the oven, pour the frosting on and spread it evenly over the top. Cool for 10-15 minutes, then lift the brownies from the pan, slice and serve.
Store remaining brownies (if there are any!) covered in the refrigerator. Enjoy.