Preheat oven to 350°F and prepare a muffin pan with liners.
Rinse the zucchini and trim off the ends. Use a fine grater to shred the zucchini. Gently wrap the shredded zucchini in a paper towel or a clean towel and squeeze out any excess water. Set aside. (I prefer to not peel the green skin off on my zucchini, but you certainly can. If you have a very large zucchini, remove any seeds prior to the grating.)
In a large bowl sift together the flour, baking soda, baking powder, cinnamon, and salt.
In a separate large bowl, add the bananas. Use a fork to mash. Add in the sugar, eggs, oil, and vanilla. Stir well (I often just use my fork) until fully combined.
Add the dry ingredients, and stir until just combined.
Add in the shredded zucchini and stir until incorporated.
Add ⅓ cup of batter to each cupcake liner.
Bake for 22-26 minutes, or until an inserted toothpick is removed with some crumbs, but not wet batter. Tops should be rounded and golden brown.