Beat eggs. Add melted butter. Add sugar, vanilla, sifted flour and baking powder. Roll into walnut-sized balls. Bake at 350 degrees for 12-15 minutes or until bottoms are slightly golden. Icing: Make a thick paste with confectioners sugar and milk. Dip tops of cookies into icing and place onto cooling rack to dry. For the holidays, sprinkle festive sugar or sprinkles while the icing is still wet, or add food coloring to the icing.