Preheat the oven to 350 degrees Fahrenheit.
Grate the zucchini and set aside. There's no need to peel it but if you don't like any green bits in the bread, you are welcome to peel!
In a large mixing bowl, whisk together all wet ingredients but keep the zucchini aside for now.
In a separate bowl, whisk together all dry ingredients except for the chopped walnuts if you're using those. Be sure to spoon and level the flour into the measuring cups and don't scoop straight from the bag.
Add the dry ingredients to the wet and mix together with a wooden spoon until combined.
Fold in the grated zucchini and walnuts and mix until well incorporated.
Add to a 9x5 loaf pan lined with parchment paper.
Top with additional chopped walnuts and a sprinkle of brown sugar if desired.
Bake for 55-65 minutes or until a toothpick comes out clean. It will rise quite a bit in the oven but will calm down slightly as it cools.
Once done, let cool for at least 1 hour before slicing. This part is annoying but it really helps ensure the bread maintains its shape and doesn't completely crumble when you slice!