Preheat the oven to 350°F and spray a muffin tray with non-stick spray. Set aside.
Sift the all purpose flour into a mixing bowl and add the white and brown sugar, baking soda, baking powder, cinnamon, nutmeg and salt and mix together.
Add shredded zucchini, buttermilk, eggs, oil and vanilla extract. Mix into a thick batter. If you have any trouble getting the batter to come together, then leave it for a minute, the zucchini will release more moisture into the batter and it will come together easily.
Add the chopped walnuts and fold in.
Divide the batter evenly between the muffin partitions. Add some more chopped walnuts directly to the tops of the muffins before baking.
Bake for 22 minutes or until a toothpick inserted into the center of one of the muffins comes out clean.
Allow to cool for a few minutes and then transfer the muffins to a wire cooling rack to cool completely.