Preheat oven to 350 degrees Fahrenheit. Grease or line muffin pans.
Use a high-powered blender or food processor to grind the oats into a flour. Transfer oat flour to a bowl, and add the baking powder, baking soda, salt, and cinnamon.
In a separate bowl, mash the bananas and add the beaten eggs, maple syrup, grated zucchini and carrots, and vanilla.
Add the dry ingredients to the wet ones and mix with rubber spatula. Note: you can now let the mixture sit for about 20 minutes to get thicker. The recipe still works if you skip this step, but the muffins will be fluffier and fuller if you let the batter sit.
Scoop the mixture into the greased muffin pans. I filled them very close to the top. If desired, press about 5 to 7 chocolate chips into some of the muffins. I made 6 muffins without chocolate and 6 with, and both kinds were equally delicious!
Bake for 30 to 35 minutes, or until a toothpick placed in the center of a muffin comes out clean.
Let them cool slightly, and enjoy! The muffins will be moist in the middle. You can store them in an airtight container on the counter or in the fridge, or freeze for busy weeks.