Preheat oven 180ºC . In a large mixing bowl, cream the butter and sugar together with an electric mixer till smooth, add the eggs and continue beating till smooth. In a bowl, mix the flour and baking powder together and add alternately with the milk to the butter mixture, beating steadily till smooth. Add the vanilla and beat till well blended. Grease and flour three 23 cm cake pans, divide the batter evenly among the pans, "spank" the bottom of the pans to distribute the batter evenly, and bake till a straw inserted in centers comes out clean, 25 to 30 minutes. Let cool completely. Meanwhile, to make the icing: melt the butter over low heat in a saucepan, add the brown sugar and milk, bring to a boil, and remove from the heat to cool. Add the powdered sugar and mix till well blended. When the cake layers are cooled, remove from the pans, place one layer on a cake plate, and spread one third of the icing on the layer. Place a second layer over the icing and spread with more icing. Top with the third layer and spread icing over the top and around the sides.