Preheat oven to 350°F (175°C). Line a muffin tin with paper liners.
In a large bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, mix together grated carrots, granulated sugar, brown sugar, vegetable oil, eggs, and vanilla extract.
Combine the wet ingredients with the dry ingredients and mix until just combined.
Divide the batter evenly among the muffin cups.
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.