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

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

In another bowl, beat granulated sugar, brown sugar, and vegetable oil until well combined. Add eggs one at a time, then stir in vanilla extract.

Gradually mix the dry ingredients into the wet ingredients until just combined. Fold in grated carrots and walnuts (if using).

Divide the batter evenly between the prepared pans. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.

Let the cakes cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.

For the frosting, beat cream cheese and butter until smooth. Gradually add powdered sugar and vanilla extract, beating until creamy.

Once the cakes are completely cool, frost the top of one layer, place the second layer on top, and frost the entire cake.