For the cake: Preheat oven to 325°. Grease a 7'' x 11'' glass baking dish with butter and set aside. Combine flour and baking powder in a small bowl and set aside. Beat egg whites in a large bowl with an electric mixer on medium speed until soft peaks form, 2-3 minutes. Increase speed to high and gradually add sugar, beating until whites are glossy, 1-1 1⁄2 minutes, then beat in yolks, one at a time. Stir in one-quarter of the flour mixture at a time. Add milk and stir until smooth. Pour batter into prepared dish. Bake until a toothpick inserted into center of cake comes out clean, 25-30 minutes. Set aside to cool in dish, then prick at 1" intervals with a toothpick.
Combine cream and condensed and evaporated milks and slowly pour over warm cake in dish. Set aside to cool, then cover and refrigerate for at least 1 hour or overnight.
For the frosting: Combine corn syrup and egg whites in a large heatproof bowl. Set bowl in a skillet of gently simmering water over medium-low heat and immediately beat egg white mixture with an electric mixer on low speed until it reaches 140° on an instant-read thermometer. Increase speed to high and beat until stiff glossy peaks form, 4-5 minutes. Remove bowl from heatand beat until meringue is cool, 2-3 minutes, then frost cake.