Allow the butter, cream cheese and the eggs (if chilled) to stand at room temperature for at least 30 minutes.
Get the ingredients ready for use by weighing/measuring each ingredient into separate bowls.
Cut two pieces of parchment paper into circles that just fit into the bottom of the cake pans. Cut another four rectangular pieces of parchment about 10 inches (25 cm) long and 2 inches (5 cm) wide.
Make the Cake
Preheat oven to 350°F (175°C).
Grease the bottom of the pans with about 1/4 teaspoon of butter each. Place a parchment paper circles into the bottom of each pan and grease the tops of the parchment paper and sides of each pan with about 1/2 teaspoon of butter.
In one mixing bowl, add the flour, sugar, baking powder, baking soda, cinnamon and salt and stir with the wire whisk until thoroughly combined.
In another mixing bowl, add the eggs and beat well with the wire whisk. Thoroughly stir in the carrots and oil and then add to the flour mixture. Stir thoroughly and then pour the batter evenly into the greased pans.
Bake for 30 to 35 minutes or until a wooden toothpick inserted near the center of each pan comes out clean, turning and swapping the positions of the pans halfway through the baking.
While the cake is baking, prepare the frosting (see below).
Cool the baked pans on a wire rack for 10 minutes. Remove the cake layers from the pans, remove the parchment paper and cool them completely on the wire rack.
Frost the Cake
If the cake layer has a domed surface, use a bread knife or a long, thin knife to cut away the dome top so that you end up with cake layers with flat surfaces ready for frosting to be applied.
On a cake board or cake stand (preferably both, with a cake board placed in the center of the cake stand), place 2 tablespoons of frosting in the center and spread it into a small circle of about a couple of inches in diameter.
Place one cake layer on the cake board/cake stand and gently use the pastry brush to brush away any loose crumbs. Gently tuck the four rectangular pieces of parchments just under the edge of the cake layer, overlapping one another to help keep the cake board/cake stand clean during frosting.
Starting from the center and moving to the edge, evenly spread about 1/2 to 1 cup of the frosting on the top of the cake layer.
Gently place the second cake layer top side down onto the first cake layer and gently use the pastry brush to brush away any loose crumbs.
Working in quarter sections, spread a thin layer of frosting onto the sides of the cake. Evenly spread about 1 to 2 cups of frosting on the top of the cake, starting from the center. Add more frosting to the sides, again working in quarter sections, blending the edges with the frosting on the top.
Slice and serve the cake immediately or chill in the refrigerator to be sliced and served up to 3 days later.
In the large mixing bowl (washed and dried after being used to make the cake batter, of course), beat the cream cheese, butter and vanilla with the stand mixer or electric hand mixer on medium speed until light and fluffy.
Gradually add the powdered sugar and beat until thoroughly combined until spreading consistency is reached (test by taking a tablespoon of frosting out of the mixing bowl and spread it on a plate to see if it is thick enough yet still easy to spread without breaking up).
Equipment Required (in order of use)
Up to 10 extra bowls to hold the ingredients
Kitchen weighing scale (preferably digital)
Baking parchment paper
2 9-inch round cake pans
2 mixing bowls
Stand mixer or hand mixer with wire whisk attachment
Silicone scraper spatula
Bread knife or long thin knife
Cake board and/or cake stand (preferably one that has a turn table)