Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, ground nutmeg, and salt. Set aside.
In a large bowl, combine the granulated sugar, light brown sugar, and vegetable oil. Beat in the eggs one at a time, then stir in 2 teaspoons vanilla extract until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing just until incorporated.
Fold in the grated carrots and chopped walnuts (if using) until evenly distributed.
Divide the batter evenly between the prepared cake pans and smooth the tops.
Bake in the preheated oven for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cakes from the oven and allow them to cool in the pans for 10 minutes. Then, turn the cakes out onto wire racks to cool completely.
While the cakes cool, prepare the cream cheese frosting. In a large bowl, beat together the softened cream cheese and unsalted butter until smooth and creamy.
Gradually add the powdered sugar, one cup at a time, beating well after each addition.
Stir in 1 teaspoon vanilla extract and continue beating until the frosting is smooth and fluffy.
Once the cakes are completely cool, place one cake layer on a serving plate. Spread a thick layer of cream cheese frosting over the top.
Place the second cake layer on top and frost the top and sides of the entire cake with the remaining frosting.
Refrigerate the cake for at least 30 minutes before serving to allow the frosting to set.