Grate the zucchini. Press out as much moisture as possible. Line a colander with paper towel and set zucchini on towel to drain further as you prepare the rest of the ingredients. Set aside in sink.
Preheat the oven to 350°F. Lightly mist a bread pan with cooking spray. Set aside.
Combine the wet ingredients. In a large bowl, mix together eggs, applesauce, olive oil, maple syrup, almond milk and vanilla. Whisk. Set aside.
Combine the dry ingredients. In a large bowl, combine whole wheat flour, all purpose flour, cinnamon, baking soda, baking powder, salt, and nutmeg. Set aside.
Fold the zucchini into the wet mixture. Pour the wet ingredients into the dry ingredients. Mix to incorporate loosely. Fold in the walnuts. Be careful not to over-mix. You'll have a few streaks of flour in the batter. The batter will also be very thick, but that's okay!
Spoon batter into greased bread pan. Use the back of a spoon to even out the batter in the bread pan. Cook approximately 45 to 50 minutes. During the last 10 minutes of baking, you may want to cover the top of the bread with foil to prevent the crust from browning too much. Remove from oven once a knife comes out of the center of the bread cleanly.
Cool the bread inside the pan on a wire rack for about 15 to 20 minutes. Turn the bread out onto the wire rack and let cool completely before cutting. Once the bread has fully cooled, cut into thick slices and enjoy with apple butter, cinnamon butter, or almond butter.