Preheat your oven to 325 degrees F. Line two 8 or 9" round pans with parchment rounds and liberally grease each pan. Set aside briefly.
In the bowl of a stand mixer, cream the butter until smooth, about 1 minute. Beat in the granulated sugar until fluffy, about 2-3 minutes. Add in the eggs, one at a time, beating well after each addition, followed by the vanilla extract. Meanwhile, sift together the flour, baking powder, salt, and spices. Alternate adding the dry mixture with the milk, ending with the milk, until the batter is smooth and blended. Stir in the apples.
Divide the batter evenly among the cake pans and bake for approximately 40-45 minutes or until a toothpick inserted near the center comes out clean or with moist - not wet - crumbs. Cool completely in the pans.
For the icing: in a bowl of a stand mixer, cream together the cream cheese and butter until fluffy and smooth, about 1 minute. Add in the brown sugar and vanilla and mix well. Gradually add in the confectioners' sugar, about one cup at a time, thinning the frosting out with the caramel sundae sauce if it becomes too thick. Frosting should be light and fluffy.
Frost the layer cake in the middle and around the tops and sides of the cake. If you have remaining icing, you can pipe little details (like flowers or swirls) around the perimeter or edges of the top and/or sides of the cake. Finish with a little extra drizzle of caramel sauce.