Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In a large bowl, beat the eggs and sugar until light and fluffy, about 2-3 minutes.
Gradually beat in the oil until well combined.
Stir in the dry ingredients until just combined.
Fold in the grated carrots and chopped pecans.
Divide the batter evenly between the prepared pans.
Bake for 25-30 minutes or until a toothpick inserted into the center of the cakes comes out clean.
Allow the cakes to cool in the pans for 5-10 minutes before transferring them to wire racks to cool completely.
To make the frosting, beat the cream cheese, butter, and vanilla extract together until smooth and creamy.
Gradually beat in the powdered sugar until well combined.
Stir in the chopped pecans.
Place one cake layer on a cake plate or stand. Spread a generous layer of frosting over the top.
Place the second cake layer on top. Spread frosting over the top and sides of the cake, smoothing it out with a spatula.
Garnish with additional chopped pecans, if desired.