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Preheat oven to 350 degrees and grease three 9" cake pans or line with parchment paper.
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Separate the 4 Eggland's Best eggs and set aside.
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In a large bowl, cream butter until light and fluffy, about 1-2 minutes. Add in vegetable oil and beat for another minute.
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Gradually add in sugar, 1/2 cup at a time, beating until well combined. Add in egg yolks, one at a time, beating well after each addition.
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In a separate bowl, sift together flour, cornstarch, baking powder, and salt. Set aside.
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In a small bowl, mix together milk, vanilla extract, and sour cream.
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Alternately add dry and wet ingredients into the creamed butter mixture, beginning and ending with the dry ingredients. Stir until just combined.
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Beat egg whites until they form stiff peaks. Gently fold egg whites into the cake batter until completely combined.
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Divide batter evenly in cake pans.
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Dollop 4-5 Tbsp of puree in each cake pan, using a toothpick or knife to swirl the puree with the batter.
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Bake for 25-30 minutes, or until a cake tester comes out clean. Allow to cool.