Preheat oven to 350 degrees then line a muffin tin with liners and set aside.
In a large bowl, whisk together eggs, sugar, and maple syrup until smooth. Add mashed banana, unsweetened applesauce, coconut oil, and vanilla then whisk until smooth.
In a separate bowl, stir together gluten-free flour, cinnamon, baking powder, baking soda, and salt then add to wet ingredients in 2 batches, stirring until the flour is just combined before adding the second batch. Add shredded zucchini then fold to combine.
Scoop batter into lined muffin tins, filling them 3/4 of the way full (I use an ice cream scoop) then bake for 17-18 minutes, rotating the muffin tin halfway through, or until a toothpick inserted into the center comes out clean. Let muffins cool in tin for 3-4 minutes before removing to a cooling rack to cool completely. Store in an airtight container on the counter for 2-3 days and/or freeze in a Ziplock freezer bag.