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Preheat oven to 350 F. Grease and flour 2 9-inch round cake pans. Additionally line the bottom with parchment paper.
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In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda and salt until well combined.
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Add the butter to the dry ingredients and using an electric mixer on low speed, mix until the mixture resembles coarse crumbs.
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Whisk together the egg, egg whites, buttermilk, lemon juice, lemon zest and vanilla in a separate bowl.
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Gradually add the wet ingredients to the dry ingredients, mixing on medium speed until the batter is well combined.
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Divide the batter evenly between the prepared cake pans.
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Bake in preheated oven for 25 to 30 minutes or until a toothpick inserted into the center comes out clean.
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Remove the cakes from the oven and let them cool in the pans for 10 minutes. Remove from pans and transfer to a wire rack to cool completely.