Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.

In a large bowl, whisk together the flour, sugar, baking powder, baking soda, cinnamon, and nutmeg.

In another bowl, mix the oil and eggs until well combined.

Add the grated carrots to the egg and oil mixture, then combine with the dry ingredients until just mixed.

Divide the batter equally between the prepared cake pans.

Bake for 30 to 40 minutes, or until a toothpick inserted in the center comes out clean.

Allow cakes to cool in the pans for 10 minutes, then turn them out onto wire racks to cool completely.

While the cakes cool, prepare the frosting by beating together the cream cheese and butter until creamy.

Gradually add the powdered sugar and vanilla, mixing until smooth.

Once the cakes are cool, spread a layer of frosting on top of one cake, place the second cake on top, and frost the top and sides.