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, salt, cinnamon, and nutmeg.
In another bowl, mix together oil, sugar, and eggs until well combined. Stir in grated carrots and vanilla extract.
Add the wet ingredients to the dry ingredients and mix until just combined.
Divide the batter evenly among the muffin cups.
Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
Let cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.