In a large bowl, whisk oil, sugar, vanilla, and egg until well combined.
In a separate bowl, combine flour, cocoa powder, baking soda, salt, espresso powder and chocolate chips.
Add the dry ingredients into the wet ingredients and stir with a rubber spatula or wooden spoon until combined. The mixture will be dry and thick.
Using the medium holes of a box grater, grate the zucchini and measure out 2 loosely packed cups. Add the zucchini (without draining) to the chocolate mixture and give it a few stirs. Allow it to sit for 5 minutes. After 5 minutes the zucchini will have released some liquid and you should be able to stir the mixture into a thick batter. Once fully combined, scoop the batter into the prepared pan and smooth it into an even layer.
Bake for 22-25 minutes, until a toothpick inserted into the center come out without raw batter on it (melted chocolate or fudgy crumbs are OK). During the last 5 minutes of bake time, begin the frosting.
Frosting:
Melt the butter in a small saucepan over medium heat. Whisk in the cocoa powder, milk and vanilla. Remove from the heat and whisk in the powdered sugar. Whisk vigorously until the icing is glossy, smooth, and fully combined. Pour the frosting over the brownies immediately after removing them from the oven. Spread the frosting into an even layer (working quickly before it firms up). Place the pan on a wire rack to cool completely.
Notes
Serving: These brownies are best served at room temperature.Storing: After cooling to room temperature, store in the refrigerator for up to 3 days or freezer for up to 3 months.