Preheat the oven to 350°F.

Spray a 9x5-inch loaf pan with nonstick cooking spray. Set aside.

Press the shredded zucchini between two layers of paper towels to remove the moisture. Add the zucchini, canola oil, brown sugar, granulated sugar, nondairy milk, flaxseed meal, applesauce, and vanilla to a large mixing bowl and whisk vigorously until smooth and combined.

Add the flour, cinnamon, nutmeg, baking powder, baking soda, and salt to the bowl. Continue whisking until the mixture is just combined. Do not overmix.

Pour the batter into the prepared loaf pan.

Bake the bread on middle rack of oven until a toothpick inserted in the center comes out clean, 55-65 minutes.

Check to see that the bread is done. Remove from oven or add time as needed.

Allow the bread to cool in the pan for 10 minutes, then release from the pan onto a cooling rack.

Allow to cool for at least 1 hour before slicing and serving. Leftover bread may be stored in a large zip-top plastic bag at room temperature for 1 day, in the refrigerator for 4 days, or in the freezer for up to 3 months.