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Separate the egg whites from egg yolks, and allow the egg whites to stand at room temperature for 30 minutes (it's easier to separate the eggs when cold, but it is better to whip the egg whites when they are at room temperature)*.
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Preheat the oven to 325. Grease three 9" round cake pans and set aside.
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In a large bowl, beat sugar, butter and oil until well blended. Add egg yolks, one at a time, beating well after each addition. Add in vanilla and almond extract. Set aside.
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In a separate bowl, sift together flour, corn starch, baking powder, baking soda and salt. Set aside.
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In a small bowl, mix whole milk, coconut milk, and Greek yogurt (or sour cream) together.
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Alternately add flour mixture and milk mixture to the creamed mixture, beating well after each addition. Once combined, add in coconut.
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Add cream of tartar to egg whites, and with clean beaters, beat on medium speed until stiff peaks form. Fold a fourth of the egg whites into the cake batter, then gently fold in remaining whites.
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Once combined, divide the batter evenly into the 3 greased cake pans. Bake 25-30 minutes, or until a cake tester comes out clean. Allow to cool at least 10 minutes before carefully removing from the pans and allowing to cool completely on a wire rack.