Preheat your oven to 180°C (350°F) and line a muffin tin with paper liners or grease it lightly.
In a large mixing bowl, combine the flour, sugar, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg.
In another bowl, whisk together the eggs, vegetable oil, milk, and vanilla extract.
Pour the wet ingredients into the dry ingredients and stir until just combined. Be careful not to overmix; a few lumps are okay.
Gently fold in the grated carrots, grated zucchini, and chopped walnuts or raisins if you're using them.
Fill each muffin cup about 2/3 full with the muffin batter.
Bake in the preheated oven for 20 minutes or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and let them cool in the muffin tin for a few minutes before transferring them to a wire rack to cool completely.Enjoy your homemade carrot and zucchini muffins!