Preheat oven to 350 degrees F (175 degrees C). Grease or line muffin cups with paper liners.
In a medium bowl, mix together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.
In a large bowl, cream together the melted butter, white sugar, and brown sugar until smooth. Beat in the eggs one at a time, then stir in the vanilla. Add the grated zucchini and carrots, and mix well.
Gradually stir the dry ingredients into the wet mixture just until blended. Fill the muffin cups about three-quarters full.
Bake for 25 to 30 minutes in the preheated oven, or until a toothpick inserted into the center of a muffin comes out clean.
Allow to cool in the pans for about 10 minutes before removing to cool completely on wire racks.
Interesting Facts
Zucchini is an excellent source of vitamin C and vitamin A.
Carrots are an excellent source of beta-carotene, fiber, and potassium.
These muffins are a great way to get your children to eat their vegetables without them realizing it!