Preheat oven to 350°F (175°C). Grease and flour a 9×5 inch loaf pan.
In a large bowl, whisk together the flour, baking soda, baking powder, salt, and cinnamon.
In a separate bowl, whisk together the granulated sugar, brown sugar, oil, egg, and vanilla extract.
Add the wet ingredients to the dry ingredients and stir until just combined.
Fold in the shredded zucchini and Greek yogurt.
If desired, fold in the chopped nuts.
Pour the batter into the prepared loaf pan.
Bake for 50-60 minutes, or until a wooden skewer inserted into the center comes out clean.
Let the bread cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.
