Cream the 1/3 cup butter and sugar together, add the well beaten eggs and mix well.  Sift flour and baking powder and add alternately with the milk to the first mixture.  Melt the tablespoon of butter together with the chocolate.  Put 1/3 of batter into a separate bowl and add the chocolate mixture.  Blend well.  To the white batter, add the vanilla.  Drop white batter, then chocolate, by spoonfuls into a well-greased, deep cake pan.  Bake at 350° about 40 minutes.