Preheat your oven to 350°F (175°C). Line a muffin tin with paper liners.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In another bowl, mix the oil, brown sugar, granulated sugar, eggs, and vanilla extract until well combined.
Gradually add the wet ingredients to the dry ingredients, mixing until just combined. Fold in the grated carrots and chopped walnuts.
Divide the batter evenly among the muffin cups, filling each about ⅔ full.
Bake for 20-25 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.