In a bowl attached to a stand mixer (or with a hand mixer), beat eggs, coconut oil, applesauce, white sugar, brown sugar, and vanilla together for several minutes until well mixed. With mixer on low speed, add in flour, baking powder, baking soda, cinnamon, salt, and mix until just combined. Remove bowl from mixer and fold in zucchini and stir until mixed in. Pour batter into prepared pan.
