Preheat your oven to 350°F (175°C). Grease a loaf pan.
In a mixing bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, combine grated carrots, oil, brown sugar, granulated sugar, eggs, and vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Pour the batter into the prepared loaf pan and bake for 50 minutes, or until a toothpick inserted into the center comes out clean.
Let the loaf cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.