Preheat the oven to 350°F and generously spray two 8- or 9-inch round cake pans (or you can use one at a time) with cooking spray. Using a stand mixer fitted with the paddle attachment (or a large mixing bowl with a hand mixer), combine the butter, oil, sugars, eggs and vanilla extract and beat on medium speed until creamy and free of lumps.
In a separate bowl, combine the flour, baking powder, baking soda, salt, cinnamon and nutmeg. Mix well. Gradually add to the butter mixture and beat on medium speed until just combined. Fold in the grated carrot.
Divide the mixture evenly between the prepared cake pans and bake one at a time in the preheated oven for 35-40 minutes, or until a toothpick inserted into the centers come out clean. Let cool in pan for 5 minutes, remove from pan and let cool completely on a wire rack. Using a serrated bread knife, cut the rounded tops off each cooled cake.
Place one cake in the center of a rotating cake stand. Spread frosting evenly and generously over the top in an even layer. Top with the remaining cake and use the remaining frosting to cover the top and sides. Refrigerate until ready to serve!