Preheat your oven to 350°F and generously grease a 9x13 inch baking pan with butter or cooking spray. This ensures your brownies won't stick and will bake evenly. Set the pan aside while you prepare the batter.
In a large mixing bowl, whisk together the vegetable oil and sugar until well combined, about 1 minute. Add the room-temperature egg and vanilla extract, whisking until the mixture is smooth and slightly pale. Gently fold in the shredded zucchini (make sure it's been thoroughly squeezed dry to avoid excess moisture) until evenly distributed throughout the mixture.
In a separate bowl, sift together the all-purpose flour, cocoa powder, baking soda, baking powder, and salt. Add the instant coffee powder and ground cinnamon to this dry mixture and whisk everything together until well combined. I like to sift the cocoa powder separately first to break up any lumps—this ensures your brownies have a rich, even chocolate color and texture without any bitter cocoa powder pockets.
Pour the dry ingredient mixture from Step 3 into the wet zucchini mixture from Step 2, folding gently with a spatula just until combined. Don't overmix—a few flour streaks are fine. Pour the batter into your prepared pan from Step 1, spreading it evenly to the corners. The batter should be thick and fudgy.
Bake for 30-35 minutes, until a toothpick inserted into the center comes out with just a few moist crumbs (not completely clean—these brownies should be fudgy and moist). The top should look set and slightly cracked. I recommend checking at 30 minutes first, as ovens vary; zucchini brownies can dry out quickly if overbaked.
Remove the brownies from the oven and let them cool completely in the pan at room temperature, about 1-2 hours. Once fully cooled, spread or pipe the cream cheese frosting evenly over the top. Cut into squares and serve.