Heat oven to 350℉. Grease baking pans with butter. Then line with parchment paper. Grease the parchment as well, and then flour the pan.
In a large bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Set the flour mixture aside.
Using a food processor fitted with the large shredding disk, shred the carrots. Transfer the shredded carrots to a bowl and set aside.
Fit the processor with the metal blade. Then add the sugar, brown sugar, and eggs to the work bowl. Process until frothy and thoroughly combined, about 30 seconds.
With the processor running, add the oil in a steady stream. Process until the sugar mixture is light in color and well emulsified, about 30 seconds.
Add the sugar mixture to the flour mixture, along with the shredded carrots and chopped walnuts. Stir everything together until the batter appears uniform and no traces of flour remain.
Spoon batter into the prepared pans. Smooth tops with a rubber spatula, and then gently tap the pans on the counter to release any air bubbles.
Bake until a toothpick inserted in the center comes out clean, about 35 to 40 minutes.
Allow the cakes to cool completely in their pans on wire racks, about 2 hours.
Once cooled, invert cakes onto the racks and discard the parchment. Place the first layer onto a cake platter and spread a thin layer of cream cheese frosting evenly over the top. Place the second layer on top. Spread the remaining frosting evenly over the top and around the sides.