Step 1: Preheat your oven to 350°F (175°C) and grease and flour two 9-inch round cake pans.
Step 2: In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, and nutmeg.
Step 3: In a large bowl, beat the granulated sugar, brown sugar, and eggs until well combined and slightly thickened.
Step 4: Slowly pour in the vegetable oil while continuing to beat the mixture on low speed.
Step 5: Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Step 6: Fold in the grated carrots and chopped nuts using a spatula until evenly distributed.
Step 7: Divide the batter evenly between the prepared pans and bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Step 8: Let the cakes cool in the pans for 10 minutes, then turn them out onto a wire rack to cool completely.
Step 9: To make the frosting, beat the softened cream cheese and butter together for 3-5 minutes until very smooth and creamy.
Step 10: Add the vanilla extract and gradually beat in the powdered sugar one cup at a time until the frosting is fluffy and spreadable.
Step 11: Once the cakes are completely cold, frost the top of one layer, place the second layer on top, and cover the entire cake with the remaining frosting.