Begin by gathering and prepping all of your ingredients according to the ingredient list above to have ready and organized for use.
Preheat the oven to 350°, and prepare a 9 by 5 inch loaf pan with parchment paper that slightly overhangs, and mist lightly with cooking spray.
To toast your walnuts, place a skillet over medium-high heat, and add in the walnuts. Stir the nuts for about 2 minutes, or until they begin to become fragrant and slightly toasted. Spoon into a small bowl to hold and cool slightly.
Next, whisk together the flour, baking powder, baking soda, cinnamon, allspice, nutmeg, and salt in a bowl, and set these dry ingredients aside for a moment.
In another larger bowl, add both the brown and granulated sugars, the eggs and the vanilla extract, and whisk for about 1 to 2 minutes, until very well blended and slightly thickened. Then, whisk in the avocado oil until incorporated.
Add in the dry ingredients, and gently whisk those in until mostly blended. Next, add in the grated zucchini and carrot, as well as the walnuts, and switching to a rubber spatula, fold those in just until blended together and combined.
Pour the batter into your prepared loaf pan, and bake the zucchini carrot bread for 1 hour and 10 minutes, or until a skewer inserted into the center of the bread comes out clean.
Allow the zucchini carrot bread to cool in the pan for 5 to 10 minutes, then carefully lift it out using the overhanging parchment paper, and allow it to cool on a wire rack completely, or just until slightly warm.
Slice the zucchini carrot bread into 9 slices, and enjoy.