- Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9 inch square pan. Sift together the flour, baking powder, baking soda, salt, cinnamon and nutmeg. Set aside.
- In a large bowl, cream together the shortening, brown sugar and white sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla. Beat in the flour mixture alternately with the milk, mixing just until incorporated. Stir in the chopped apples.
- Spread batter evenly in prepared pan. Bake in the preheated oven for 35 to 40 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool.
- To make the frosting: In a medium bowl, combine 1/4 cup shortening, confectioners’ sugar, cinnamon and nutmeg. Beat until light and creamy. Beat in the milk, one tablespoon at a time, until desired spreading consistency is achieved. Spread over top of cooled cake.