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Cake:
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Preheat oven to 350 degrees.
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Separate egg yolks and whites, keeping whites at room temperature.
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In bowl of an electric mixer, cream sugar and butter together until pale yellow and fluffy.
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Add egg yolks and beat until fluffy again, 2 to 3 minutes on medium-high speed.
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In a separate bowl combine flour and baking powder.
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In a third bowl mix milk and vanilla.
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Alternately add the flour mixture and the milk mixture to the butter mixture (a fourth at a time) until all are combined.
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Beat until smooth after each addition.
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Beat egg whites with cream of tartar until soft peaks form and, using a large spatula, gently but thoroughly fold into flour-and-butter mixture.
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Grease bottom of a 9- by 13-inch metal baking pan.
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Pour in batter and bake for approximately 25 minutes, until golden brown. Allow to cool.
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(May also be baked in an 11.5- by 17.5-inch sheet pan for 20 minutes; this size rises very evenly, helpful for inexperienced cooks.).
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Three Milks:
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Stir the milks together thoroughly; do not beat.
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Do not refrigerate canned milks before using.
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Cream Icing:
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Whip cream and sugar together until stiff.
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When cake is cool, slice or peel off the thin top crust.
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Ice sides first, creating a small lip on top to catch milk mixture.
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Pour milk mixture evenly over top of cake (if necessary, poke holes in cake with a knife or toothpick to facilitate soaking; you will probably need only 3/4of mixture).
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Finish icing top.
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Refrigerate.
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(If using an 11.5- by 17.5-inch pan, cut cake in half to make 2 equal pieces. Soak first layer, ice top if desired, and place second layer on top of it. Proceed as above.) Serves 12.