Preheat the oven to 350°F (175°C). Line a muffin tin with paper liners or grease it lightly with cooking spray.
In a large mixing bowl, combine the mashed bananas, grated zucchini, vegetable oil, brown sugar, granulated sugar, eggs, and vanilla extract. Mix until well combined.
In a separate bowl, whisk together the flour, baking soda, baking powder, salt, and cinnamon.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Be careful not to overmix.
If using, fold in the chopped nuts and chocolate chips.
Divide the batter evenly among the muffin cups, filling each about 2/3 full.
Bake in the preheated oven for 18-22 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Allow the muffins to cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely.