Preheat the oven to 350°F and grease two 8 inch round cake pans. Grease these well or use parchment paper and baking spray. See the post for the how-to on preparing the pans.
Mix the cake ingredients in order, stopping after the carrots; a stand mixer works best for mixing this.
Fold in the walnuts.
Pour ½ the batter in one cake pan and the rest in the other. This will be a thick batter, may need to spread it into the pan.
Bake in the oven at 350°F for 35 minutes or until poked in the center with a toothpick, the toothpick comes out clean.
Let the cakes cool for 5-10 minutes and carefully release the cake and place it on a wire rack for 1-2 hours to cool completely.
While the cakes are cooling, prepare the icing; begin by creaming together the butter and cream cheese.
Add in the vanilla and powdered sugar, whisking on high with a stand mixer until the icing is formed.
Fold in the walnuts.
Release one of the cakes from the cake pan, and then ice the top of it with a portion of the icing.
Place the second cake on top and then continue icing the entire cake.
If you prefer, this can be the crumb coat and make a second batch of icing for a final coat.
This can be chilled in the fridge and served cold or served at room temperature.
Video
Notes
If you want to have a crumb coat + final coat of icing, double the recipe for the icing. The photos you see in this post have 2 layers of icing, a crumb coat plus an additional coat.If you do this, frost the cake then let it harden in the fridge for about 30 minutes to 1 hour then frost again with a final coat.