Makes about 6 cups batter.
Set oven rack in the lower third of the oven. Preheat oven to 350°F. Grease or spray pans; line bottoms with parchment paper. Grease and flour or spray again.
In medium bowl, lightly combine eggs, about 1/4 of the sour cream and the vanilla extract. In mixer bowl, combine flour, sugar, baking powder, baking soda and salt. Mix on low speed 30 seconds to blend. Add butter and remaining sour cream; mix on low speed until dry ingredients are moistened. Increase mixer to medium speed and beat 1 minute to aerate and develop the structure. Scrape down sides of bowl. Gradually add the egg mixture in 2 batches, beating for 30 seconds after each addition until fully incorporated, scraping down the sides. Scrape batter into the prepared pan, smoothing evenly with a rubber spatula. The pan will be about half full.
Bake for 35 to 40 minutes or until a wooden toothpick inserted in the center comes out clean and the cake springs back when pressed lightly in the center. Let the cake cool in the pan on a rack for 10 minutes. Loosen the sides with a small metal spatula and invert onto a greased wire rack. To prevent splitting, reinvert so that the top is up; cool completely before wrapping airtight. Wrapped cake can be stored 1 day at room temperature; 3 days refrigerated; 2 months frozen.