Preheat the oven to 350ºF. Line two muffin tins with a total of 16 paper cups. (Alternately, grease 16 muffin cups with cooking spray.)
In a large bowl, whisk together the flour, sugar, baking soda, cinnamon and salt.
In a separate medium bowl, whisk together the mashed bananas, buttermilk, eggs, melted butter and vanilla. Stir the banana mixture into the dry ingredients.
Shred the zucchini on the small hole of a box grater. Measure out 1 1/2 cups of shredded zucchini then squeeze it in a dish towel to ring out excess moisture.
Fold the zucchini and chopped nuts (optional) into the batter.
Divide the batter among the muffin tin cups, filling each about 3/4 full.
Bake the muffins for 22 to 26 minutes until a toothpick inserted comes out clean. Remove the muffins from the oven and let them cool slightly before serving.