Preheat oven to 350°F. Grease or spray with non-stick cooking spray loaf pan(s). Line pan with parchment paper, leaving excess over long sides of pan.
On a flat surface, shred zucchini on a box grater using the largest hole grating size. Transfer zucchini to a clean kitchen towel. Place zucchini in the center of the towel, spreading it out lengthwise. Roll zucchini up in the towel. Grasping both ends, and using both hands, twist the towel like you are wringing it out. Repeat wringing until little to no liquid comes out. Spread zucchini out on a dry towel until you're ready to add it to the batter.
In a large bowl, lightly beat the eggs. Stir in oil, applesauce, vanilla, orange zest, white sugar and brown sugar. Fold in zucchini.
In medium bowl, combine flour, cinnamon, salt, baking powder and baking soda. Add to wet ingredients and mix until just combined. Transfer batter to prepared loaf pan(s).
Bake on center rack of oven for 1 hour to 1 hour and 15 minutes, or until toothpick inserted in center of loaf comes out clean.
Cool 15 minutes in pans. Remove from the pans and cool completely on wire racks.
Store on the counter in airtight container for up to 3 day or refrigerate for up to one week.
This recipe makes 2 medium bread loaves (9 x 4.5 x 2.5 inch loaf pan). Alternately, make 1 larger loaf (9 x 5 x 3 loaf pan) or 4 mini-loaves.Bake time for large loaf is 1 1/2 hours. Bake time for mini-loaves is 50 minutes.Nutrition information is for 2 loaves, cut into 12 slices each.