Preheat oven to 350F°/177C°.
Spray a 9- by 13-inch cake pan with baking spray or grease with butter and flour. Set aside
Sift the flour, baking powder, and salt into a large bowl. Set aside.
Break the eggs, then separate the egg whites from the yolk. Place in a medium bowl and add the egg whites to another bowl.
Beat the egg whites at high speed until soft peaks form.
Using a hand mixer whisk together the egg yolks and sugar until the yolks become pale yellow. Add the milk and vanilla extract to the egg yolk mixture.
Then slowly pour the egg yolk mixture into the flour mixture; stir to combine.
Gently fold in the soft peak-egg white mixture to the batter until just combined. Do not over-mix.
Pour cake batter into the greased pan and place in the oven. Bake for about, 35 to 40 minutes or until a toothpick inserted into the center comes out clean.
In a medium bowl or pouring jar - Combine evaporated milk, heavy cream, and condensed milk.
Using a wooden skewer, pierce the cake with holes then slowly pour ALL the milk all over the surface of the cake. Making sure to pour near the edges and all around the cake.
Refrigerate the cake for at least an hour or overnight, for the milk to fully penetrate the cake.
Combine the caramel/dulce de leche, water, and rum- microwave for about 30 seconds-this makes it easy to mix.
Pour or spread the mixture on the cake cover with a plastic wrap and refrigerate until ready to serve at least four hours or preferably overnight.