To make the cake: Preheat the oven to 350 degrees F. Lightly grease and flour a 9 by 13-inch baking dish and set aside.
In the bowl of a mixer, beat the egg whites on low speed until soft peaks form. Add the sugar gradually with the mixer running and peak to stiff peaks. Add the egg yolks 1 at a time, beating well after the addition of each.
Sift together the flour and baking powder and add to the egg mixture, alternating with the milk. (Do this quickly so the batter does not lose volume.) Add the vanilla. Bake until golden, 25 minutes.
To make the cream topping: In a blender, combine the evaporated milk, condensed milk, and heavy cream and blend on high speed.
Remove the cake from the oven and while still warm, pour the cream mixture over it. Let sit and cool to room temperature. Cover and refrigerate until well chilled, at least 4 hours or overnight.
To make the icing: Once the cake is completely chilled, in a saucepan combine the water and sugar. Bring to a boil. Reduce the heat and stir to dissolve the sugar. Cook until the mixture reaches the soft ball stage, 235 to 240 degrees F. Remove from the heat. In a medium bowl, beat the egg whites to soft peaks. While beating, add the hot syrup in a stream. Beat until all the syrup has been added, the mixture cools, and a glossy icing forms.
To assemble: Remove the cake from the refrigerator and spread the icing evenly across the top. Arrange the mango and papaya slices over the top and serve.