Preheat your oven to 350°F (175°C). Line a muffin tin with paper liners.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, beat the eggs and mix in the granulated sugar, brown sugar, and vegetable oil until well combined.
Stir in the grated carrots and vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Divide the batter evenly among the muffin cups, filling each about ⅔ full.
Bake for 20 minutes, or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.