Preheat the oven to 350°F. Heavily oil a Bundt pan or line 2 (9-inch) cake pans with parchment paper, and set pans aside. On a separate piece of parchment paper, sift together the cake flour, baking powder, and salt, then set aside. In the bowl of an electric mixer fitted with the whisk attachment, cream the butter at medium speed until it is soft and fluffy. Slowly add the sugar.

Meanwhile, combine the milk, vanilla extract, and vanilla bean seeds. Stop the mixer and add half of the milk mixture (it’s worth stirring it a little by hand here so that it doesn’t splash all over your kitchen), then mix at low speed until it is incorporated. Use the parchment paper as a funnel to add half of the flour mixture and mix slowly. Repeat the process by adding the rest of the milk mixture, stirring slowly, then adding the rest of the flour. Remove the bowl from the mixer, and use a large rubber spatula to stir until smooth.

Transfer the batter to a large bowl and set aside. Thoroughly rinse and dry the mixer bowl and whisk attachment. Place the egg whites in the bowl and mix at low speed; increase speed to medium. (After a few minutes, the egg whites will hold a medium peak.) Fold the whipped egg whites into the batter in thirds with a large rubber spatula, gently folding the batter after each addition.
Pour the batter evenly into the prepared cake pan. Bake 35–40 minutes until the cake is golden brown on top and a toothpick inserted in the center comes out clean. Cool the cake on a wire rack to room temperature.

While the cake bakes, prepare the Dulce de Leche. Stir together the milk, sugar, baking soda, vanilla bean pod and seeds, and salt in a large saucepan. Bring to a boil over medium heat. (The mixture will bubble up high.) Stir, and reduce the heat to low, letting the sauce simmer. Skim it occasionally with a strainer, and stir the bottom of the pan with a wooden spoon or heat-proof spatula to make sure the milk solids don’t scorch.

After about 1 hour, remove the vanilla bean pod. (The sauce will slowly turn light brown, reduce, and turn honey-colored. You want it to reach a dark amber color but still be pourable.) The total cooking time is about 1½ hours. For a thin, sweet sauce, 1½ hours will do it. If you like a thicker texture, keep cooking and stirring. Once the sauce is amber in color and has reached desired thickness, remove it from the heat and let it to cool for 5 minutes. Stir in the milk chocolate, if desired.

To assemble, place a cake plate or sturdy paper plate over the bottom of the cake pan. Invert the cake onto the plate. Pour the Dulce de Leche over the cake, slice and serve.