Preheat your oven to 350°F (175°C) and grease a 9x5 inch loaf pan or line it with parchment paper for easy removal.
Grate the zucchini using a box grater or a food processor. Once grated, place the zucchini in a clean kitchen towel and pat it dry to remove excess moisture. This step is crucial to avoid a soggy bread.
In a large mixing bowl, combine the sugar and olive oil. Whisk together until well mixed. Then, add the beaten eggs, milk, vanilla extract, and mashed bananas. Stir until everything is well combined.
In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, cinnamon, and salt. This step ensures that the leavening agents are evenly distributed throughout the flour.
Gradually add the dry ingredients to the wet ingredients, mixing gently with a rubber spatula until just combined. Be careful not to overmix; a few lumps are perfectly fine.
Gently fold the shredded zucchini into the batter until evenly distributed. The batter will be thick and chunky, and that's just how you want it!
Pour the batter into the prepared loaf pan, smoothing the top with a spatula.
Place the loaf pan in the preheated oven and bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Once baked, remove the bread from the oven and let it cool in the pan for about 10 minutes. Then transfer it to a wire rack to cool completely before slicing.