Preheat your oven to 350°F (175°C). Line a muffin tin with paper liners or grease it lightly.
In a large bowl, combine the grated zucchini, diced apples, granulated sugar, brown sugar, vegetable oil, eggs, and vanilla extract. Mix until well combined.
In another bowl, whisk together the flour, baking soda, baking powder, cinnamon, salt, and nutmeg.
Gradually add the dry ingredients to the wet ingredients, stirring just until combined. Be careful not to overmix. If using, fold in the chopped nuts.
Divide the batter evenly among the prepared muffin cups, filling each about 2/3 full.
Bake for 20-25 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 before transferring them to a wire rack to cool completely.