Heat oven to 350°F. Line a 12-cup muffin pan with liners.
Grate zucchini and squeeze out excess liquid until fairly dry.
Whisk eggs, both sugars, oil, yogurt, and vanilla until smooth.
In another bowl, whisk flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
Fold dry ingredients into the wet mixture just until combined.
Gently stir in zucchini, chocolate chips, and walnuts if using.
Scoop batter into liners, filling each about three-quarters full.
Bake 17–19 minutes, until a toothpick comes out with a few moist crumbs.
Cool 5 minutes in pan, then transfer muffins to a rack to finish cooling.