Line cupcake pans with cupcake liners and pre-heat oven to 350 degrees. Sift together flour, baking powder, baking soda, cinnamon, and nutmeg.
Peel the carrots and coarsely chop. Add the carrots to a food processor or blender and blend until pureed. Add water a teaspoon at a time to thin if needed.
In an electric mixer cream eggs, sugars and vanilla extract until smooth. Add oil and mix until combined.
Add dry ingredients gradually until combined. Pour in pureed carrots and mix until smooth.
Pour into cupcake tins using a 1/4 cup measuring cup and fill 3/4 the way full.
Bake for 20-25 minutes or until an inserted toothpick comes out clean.