Preheat oven to 325 degrees. Beat the already beaten egg with sugar until light in color. In a seperate bowl, sift flour baking powder and salt. Blend with the egg mixture and fold in the apple, nuts, and vanilla. Pour into a greased shallow 1 1/2 quart baking dish and bake 30 minutes. At serving time, whip the cream, flavor with rum and garnish the cooled pudding.