Preheat oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or lightly grease the cups.
In a medium bowl, whisk together flour, baking soda, baking powder, salt, and cinnamon.
In a large bowl, whisk together mashed bananas, shredded zucchini, brown sugar, granulated sugar, oil, eggs, and vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients and stir until just combined.
Fold in any optional mix-ins if desired.
Divide the batter evenly among the muffin cups, filling each about ¾ full.
Bake for 18–22 minutes or until a toothpick inserted into the center comes out clean.
Cool in the pan for 5 minutes before transferring to a wire rack to cool completely.