Preheat the oven to 350 degrees F. Grease and line two 8-inch round cake pans.
Mix brown sugar and cinnamon together.
Beat butter and sugar together in the bowl of a stand mixer fitted with a paddle attachment until smooth and creamy. Add the eggs one at a time, beating until incorporated. Add the vanilla extract and beat to incorporate.
Sift flour and baking powder together in a bowl. Stir into the creamed butter mixture. Add the milk to the batter and mix until smooth.
Pour ¼ of the batter into one of the cake pans. Add ¼ of the apples and ¼ of the brown sugar mixture on top. Lightly pat the apples into the batter. Pour another ¼ of the batter of the apple layer, and top with another ¼ of the apples and brown sugar mixture. Repeat in the second cake pan with the remaining batter, apples, and brown sugar.
Bake in the preheated oven for 30-40 minutes, until a toothpick inserted into the center comes out clean. Remove from the oven and set aside to cool.
Place butter, vanilla, cinnamon, confectioner’s sugar, and 1 tablespoon of cream into a stand mixer fitted with the paddle attachment. Turn the mixer on and slowly combine all the ingredients. If the frosting seems too thick, add the remaining tablespoon of cream. Turn the mixer on high and mix for 1-2 minutes, until the frosting is light, fluffy, and spreadable.
To assemble the cake, place the first layer of cake on a cake stand. Drizzle with up to 3 tablespoons of caramel. Spread frosting over the top. Place the remaining layer of cake on the frosting. Drizzle with another 3 tablespoons of caramel and serve immediately.