In a mixing bowl cream together the softened butter and sugar, then beat in the egg. Mix together the dry ingredients and stir them into the butter, sugar and egg mixture.
Mix in the diced apple pieces and the chopped walnuts. Grease your baking pan and pour the batter into it. Bake at 350 degrees for about 30 minutes. Make sure the cake is done in the center.
Use a saucepan in which to heat all the sauce ingredients. Heat over low-to-medium heat and stir until the sugar is dissolved. Pour or ladle the warm sauce over the cake and enjoy a good dessert.