Preheat the oven to 325 degrees F. In a medium sized mixing bowl, combine the flour, baking powder, and salt. Whisk to combine and then set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and the sugar. Mix on medium-high speed for about 3 to 5 minutes, until the mixture is light and fluffy.
Add the eggs, one at a time, scraping down the sides and bottom of the bowl to make sure all of the butter and sugar are mixed well with the eggs. Add the vanilla.
With the mixer on medium-high speed, add the dulce de leche and mix for another 3 minutes. The mixture will get a little lighter in color and will increase in volume.
With the mixer on low speed, alternately add the dry ingredients and the milk, starting and ending with the dry mixture. Mix until just combined.
Pour the batter into your three 8-inch pans (or four 6-inch pans) with the cooled shortbread crust and bake until a toothpick inserted in the center of the cake comes out with a few moist crumbs on it, about 30 to 35 minutes.
Allow the cakes to cool in the pan on wire racks for about 10 to 15 minutes and then invert onto wire racks (TIP: spray the racks with non stick spray) and allow to cool completely.
Cakes can be made ahead of time and wrapped in plastic wrap and frozen until ready to use. Be sure to give the cakes about 30 to 60 minutes at room temperature before stacking and decorating.