Preheat the oven to 180°C and line a 12-hole muffin tray with paper cases or lightly grease it.
In a large bowl, combine the flour, oat bran, cacao powder, baking powder, baking soda, salt, and cinnamon. Mix well and set aside.
Grate the zucchini using a box grater. Place the grated zucchini into a sieve, then use your hands to press and squeeze out as much liquid as possible. This step is important to prevent soggy muffins.
In a separate bowl or large jug, add the milk, oil, vanilla, and eggs. Use a fork to whisk the eggs and combine everything together.
Pour the wet mixture into the dry ingredients. Stir gently until just combined -don't overmix.
Add the grated zucchini and ¼ cup of choc chips, then fold them through the batter.
Divide the batter evenly among the muffin tray and sprinkle the remaining choc chips evenly over the muffins. Bake for 15 minutes. To test the batter is cooked, insert a skewer and if it comes out clean, they're cooked.
Remove from the oven and allow the muffins to cool in the tray for 5 minutes before transferring them to a wire rack to cool completely.