Preheat oven to 350°F (175°C). Grease a muffin tin or line with paper liners.
In a large bowl, mix together the flour, sugar, baking powder, baking soda, salt, cinnamon, and nutmeg.
In another bowl, beat the eggs, then add the oil and vanilla extract.
Stir the wet ingredients into the dry ingredients until just combined.
Fold in the grated zucchini.
Spoon the batter into the prepared muffin tin, filling each cup about ⅔ full.
Bake for 20 minutes or until a toothpick inserted into the center comes out clean.
Let cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.