Heat the oven to 350°F. Prepare the Cake Batter: Prepare two 8 (or 9) inch round cake pans by greasing the bottom and sides with softened butter or shortening, then put a round of parchment paper on top. Spray the parchment with cooking spray then lightly dust parchment and sides with flour. Set-aside. n a medium bowl combine the flour, baking soda, salt, cinnamon, and nutmeg; whisk or sift until blended.
In a large bowl or the work bowl of your stand-up mixer, combine the oil and sugars using a medium-low speed on either your standing mixer or a hand mixer. Combine the vanilla with the eggs and add, one egg at a time, to the mix of oil and sugar making sure the egg is blended in before adding the next one. Once the eggs are incorporated, slowly add the dry ingredients and continue to mix, at medium-low speed, until combined and the batter is smooth. Stir in the carrots and walnuts, mix to combine.
Divide the batter between the prepared cake pans and place in the middle of the preheated oven; bake until the cake springs back when lightly touched in the center, or when a toothpick, inserted in the center, comes out clean., 35 to 45 minutes.
Cool cakes in the pan for 15 minutes, then turn onto a cooling rack, remove the parchment paper, and allow the cakes to cool completely.
Prepare the Frosting: Using your hand mixer and a large bowl or work bowl of your free-standing mixer, beat the cream cheese until light and fluffy; beat in the powdered sugar and vanilla; beat until smooth. Add the cream and beat for about 1 minute. Chill until ready to use.