Position rack in bottom 1/3 of oven and preheat the oven to 350 degrees F.

Lightly grease a 13 by 9-inch baking pan with the shortening. Add 1 tablespoon of the flour to the greased pan and shake it around to coat the entire pan with the flour. Shake out excess flour. Set aside.

In the bowl of an electric mixer fitted with a whisk attachment, beat the egg whites on medium speed until soft peaks form. Reduce the speed to low and gradually add the sugar with the mixer running, beating until stiff peaks form.

Add the egg yolks, 1 at a time, beating well after each egg is added. In a small mixing bowl, sift together the 2 cups flour and baking powder. Add the flour mixture to the batter in stages, alternating with the whole milk, beginning and ending with the flour. (Do this quickly so that the batter does not lose its volume.) Add 1 teaspoon of the vanilla extract. Pour the batter into the prepared pan and place in the oven. Bake for 25 to 30 minutes, until a toothpick inserted into the center comes out clean. Remove the cake from the oven and place on a wire rack to cool for 10 minutes.

In a blender, combine the evaporated milk, sweetened condensed milk, and 2 cups of the heavy cream. Cover and blend on high for 45 seconds.

Remove 1 1/2 cups of the milk mixture, cover, and refrigerate until ready to serve the cake.

Pour 1/2 of the remaining milk mixture over the warm cake.

When the cake has soaked up most of the liquid, pour the remaining half of the milk mixture over the cake, and cool to room temperature. Cover and refrigerate until well chilled, at least 4 hours or overnight.

When ready to serve, beat the remaining cup of heavy cream in the electric mixer until soft peaks form. Add the confectioners' sugar and remaining 1/4 teaspoon of vanilla, and beat until stiff peaks form. Spread the whipped cream over the chilled cake.

Serve the cake with the reserved chilled milk sauce.