Book club meeting. Mother's Day brunch. A well-deserved raise. Cream cheese frosting is always the answer.
Let eggs stand at room temperature for 30 minutes. Preheat oven to 350°. Grease a 6x3-inch springform or round cake pan. Line bottom with parchment paper; grease again. Set aside. (If available, prepare three pans.)
In a medium bowl, stir together flour, granulated sugar, baking powder, cinnamon, baking soda and salt; set aside. In a small bowl, lightly beat eggs. Stir in carrot and oil. Stir egg mixture into flour mixture until combined. Spread one-third of the batter in the pan. Chill remaining batter (or spread it in the other two pans, if using).
Bake for 20 minutes or until a wooden toothpick inserted near center comes out clean. Cool cake in pan on wire rack for 10 minutes. Run knife around cake to loosen. Remove cake from pan; gently peel off paper. Cool completely on wire rack. If using one pan, wipe it clean and bake two more layers with remaining batter.
For frosting: In a medium bowl, beat cream cheese, butter and vanilla with an electric mixer on medium speed until light and fluffy. Gradually beat in powdered sugar to reach spreading consistency.
To assemble, place one cake layer, bottom side up, on a platter. Spread with about one-third of the frosting. Repeat with another cake layer and another one-third of the frosting. Top with the remaining cake layer, rounded side up, and remaining frosting. Sprinkle with walnuts. Store, covered, in the refrigerator.
If you only have one sprigform pan, chill 2/3 of the batter while the first cake layer bakes. After baking, wipe out pan, repeat step one, spread another 1/3 of batter into pan, bake as directed. Repeat for the 3rd cake layer.