Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, salt, and ground cinnamon. Set aside.
In a large bowl, combine the granulated sugar, light brown sugar, mashed bananas, vegetable oil, eggs, and vanilla extract. Mix until smooth and well combined.
Add the dry ingredients to the wet ingredients and gently fold together until just combined. Do not overmix.
Fold in the shredded zucchini and chopped walnuts if using.
Divide the batter evenly among the prepared muffin cups, filling each about 3/4 full.
Bake in the preheated oven for 18 to 20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and allow them to cool in the pan for 5 minutes.
Transfer the muffins to a wire rack to cool completely before serving.