Finely grate or shred the zucchini, using a sharp knife, vegetable peeler, cheese grater, or slicer/shredder attachment on your KitchenAid. Place the shredded zucchini in a strainer and, using paper towels or a clean, absorbent cloth, gently squeeze as much moisture out of the zucchini as you can. Allow to rest on paper towels to continue to soak any excess water.
Preheat oven to 350℉.
Using a mixer, cream together the sugar and butter. Mix in the eggs until the mixture is completely blended and has a creamy consistency.
Then, stir in the vanilla and grated zucchini.
Turn off the mixer for the time being and add all of the dry ingredients on top of the zucchini mixture: the cocoa powder, flour, salt, and baking powder. Gently beat on low speed, or stir by hand, until all ingredients are fully-incorporated. The batter should appear to be rich and chocolatey.
Gently fold the chocolate chips into the batter.
Pour the brownie mix into a 9" baking pan and bake at 350℉ for 20-25 minutes.
Important Note: Do not over-bake! The batter may be somewhat wet in the middle when done, as these brownies have a very fudgy consistency (hence, the name). However, the brownies are done when the edges are firm and begin to pull away from the pan.
Remove from oven and allow to cool on wire rack for at least 30 minutes prior to cutting and serving. Store leftovers (if there are any) in the fridge.