Preheat your oven to 350°F (175°C). Line a 12-cup muffin tin with cupcake liners.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Set aside.
In a large mixing bowl, whisk together granulated sugar, brown sugar, oil, eggs, and vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix!
Fold in the grated carrots until evenly distributed.
Divide the batter evenly among the cupcake liners, filling each about ¾ full.
Bake for 18-22 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and let the cupcakes cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely.