Preheat your oven to 350°F and spray 5 jumbo muffin cups or ramekins with cooking spray.
In a small bowl, prepare flax eggs by mixing ground flaxseed with water. Set aside to thicken.
Pour 2 cups of oats into a food processor or blender, and process until they turn into a fine flour.
In a large mixing bowl, combine the oat flour, the remaining ½ cup of oats, walnuts, raisins, cinnamon, baking powder, and salt.
Grate zucchini and carrot, then squeeze excess water from the zucchini using a towel.
Add the grated vegetables to the dry mixture.
In another bowl, mash the bananas and whisk together with apple sauce, maple syrup, vanilla, and prepared flax eggs.
Pour the wet ingredients into the dry ingredients. Stir until just combined, avoiding overmixing.
Divide the batter evenly among the muffin cups, filling them almost to the top.
Bake for 26 minutes, or until a toothpick inserted in the center of a muffin comes out clean.
Allow muffins to cool in the pan for 5 minutes before transferring to a wire rack to cool completely.