Preheat oven to 350 °F. Grease and flour two 8 or 9 inch round pans or one 9×13-inch pan.

Sift the cake flour and then measure out 3 cups into a large mixing bowl.

Add the white sugar, baking powder, cinnamon, nutmeg, and salt to the sifted flour and whisk together to combine.

In the bowl of an electric mixer combine brown sugar, butter, applesauce, and buttermilk. Beat for 2 minutes.

Add the eggs and vanilla and beat for 2 more minutes.

With the electric mixer on low, gradually add the dry ingredients to the wet ingredients. Continue mixing until the batter is smooth.

Fold the apples into the batter.

Pour the cake batter into the prepared pans. Bake 25 to 30 minutes for round pans or 30 to 40 minutes in a 9×13 pan or until cake tests done.

Allow round pans to cool at least 15 minutes. Run a knife around the perimeter of the pans and turn onto a cooling rack. Cool completely.

In a medium-sized saucepan, melt the butter. Add brown sugar and bring to a boil. Boil for exactly 2 minutes, stirring continuously. Add the milk and bring back to boiling. As soon as it has reached the boiling state, remove it from the heat. Add the powdered sugar and vanilla. Spread icing on cooled cake.

Prepare the Caramel Icing as instructed above and allow it to cool. Add the icing to the bowl of an electric mixer and add 1¼ cups powdered sugar or enough to get a spreading consistency. Add additional milk if frosting becomes too thick. Frost the cooled cake or store covered in the refrigerator until needed.

The cake can be stored at room temperature for up to 3 days.