Preheat oven to 375° F and prepare two standard muffin tins
In a bowl, combine the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Set aside
In a large bowl (or your stand mixer), mix together the eggs, brown sugar, white sugar, and vanilla until smooth and creamy
Add oil and mix until well incorporated.
Add the flour mixture to the wet ingredients, one cup at a time, and mix
Once combined, stir in the grated carrots and toasted pecans using a rubber spatula
Pour batter into the prepared cupcake tins, filling each cavity about two-thirds full
Bake for 20-24 minutes, or until a toothpick inserted into the middle of the cupcake comes out clean
Let the cupcakes cool for 10 minutes before removing from the tin
Let the cupcakes cool completely before frosting with cream cheese frosting