Preheat the oven to 350F (180C or 170C fan forced). Line a 12-cavity muffin pan with muffins papers.
Blot the grated zucchini with paper towel to remove any excess liquid. It shouldn't be bone dry, but you don't want pools of water at the bottom of your measuring cup.
In a medium bowl whisk together the flour, cocoa, baking powder, baking soda and salt. If the cocoa appears lumpy, sift it first.
In a large bowl whisk together the oil, brown sugar, granulated sugar, eggs, vanilla extract and milk. When finished you should no longer have lumps of brown sugar or pieces of egg.
Carefully whisk the dry ingredients into the wet ingredients until smooth.
Stir in the grated zucchini.
Spoon the batter evenly between the 12 lined cupcake papers. Each should be about ⅔ to ¾ full. You may need to make up to 14 cups.
Bake in the preheated oven for 18-22 minutes or until the tops look set and an inserted toothpick comes out clean.
Cool the cupcakes in the pan for at least 10 minutes, then transfer to a wire rack to continue cooling