In the bowl of a blender, place the eggs, rolled oats, neutral oil, sugar, vanilla extract, baking soda, baking powder, cinnamon, ginger, and 1 cup of the shredded zucchini. Blend everything on high for a minute or two until a smooth batter forms.
Add the reserved 1/2 cup shredded zucchini and the diced apple (with the peel on). Gently pulse 2 to 3 times until mixed in but not chopped.
Place 10 muffin cups into a muffin tin and pour the batter divided evenly between the cups. Sprinkle the tops with extra oats and gently press them down.
Bake for about 30 to 35 minutes until a toothpick comes out clean (ours took 34 minutes). Remove from the muffin tin and allow them to cool before serving. Store refrigerated for about 1 week or frozen for several months.