Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9×13-inch baking pan.
Mix together flour, baking powder, and salt in a bowl. Stir together 1/2 cup milk with 1 teaspoon vanilla in a glass measuring cup.
Beat egg whites with an electric mixer on medium-high speed until soft peaks form. With mixer running, add 1 cup sugar, 1 tablespoon at a time, and beat until whites are very stiff but still glossy, about 8 minutes. With mixer on low, add yolks, 1 egg at a time, beating until combined. Add flour mixture, 2 tablespoons at a time, alternating with milk mixture just until batter is smooth (be careful not to beat so much it deflates).
Pour batter into prepared pan and bake in middle of oven until a toothpick inserted into center comes out clean, 27 to 30 minutes.
Cool cake 30 minutes in pan on a rack (it will shrink), then invert onto rack to cool completely. When cooled, return cake to baking pan. Poke holes all over cake with fork.
Stir together condensed milk, evaporated milk, and remaining 1/2 cup whole milk, and pour over cake. When cake absorbs milk mixture, 5 to 10 minutes, cover pan with plastic wrap and chill at least 2 hours or up to 8 hours.
Whip heavy cream with remaining 1/4 cup sugar and remaining teaspoon vanilla with electric mixer on medium speed until stiff, then spread evenly over cake. Serve as is or top with fresh fruit.
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