Tres Leche Cake (three Milks Cake)

Preheat oven to 350 degrees. Sift together the cake flour and baking powder. In a large mixing bowl, cream the 1 cup sugar and the butter with an electric mixer until well blended. Add the eggs and 1/2 teaspoon vanilla extract, and beat until foamy. With a rubber spatula, gently fold in the flour mixture in increments, alternating with 1/3 cup milk, until the batter is smooth. Pour cake batter into a lightly greased cake pan or baking dish, 7 by 11 by 2 inches, and bake for 30 minutes, or until a toothpick inserted in the center comes out clean and the top springs back when pressed. Allow cake to cool in the pan on a wire rack for 20 minutes, then invert onto a serving platter. Pierce the cake with a fork in many places, and allow it to cool completely. In a medium mixing bowl, whisk together the condensed milk, evaporated milk, 1 cup milk and rum until well blended. Pour syrup evenly over the cake a little at a time, until it is saturated; you may not need the entire amount. Refrigerate, covered in plastic wrap, for at least 3 hours. In a large mixing bowl with an electric mixer, whisk the heavy cream until it begins to thicken. Add 1 teaspoon sugar and 1/2 teaspoon vanilla extract, and continue whisking until stiff peaks form. Using a spatula, spread the cream over the top and sides of the cake. Serve, cut into squares.