For the apple cinnamon cake: Preheat the oven to 350 degrees F. Spray two 8-inch round cake pans with baking spray or line with parchment.
Mix the brown sugar and cinnamon together in a bowl. Set aside.
Beat the butter and granulated sugar together in the bowl of a stand mixer fitted with the paddle attachment until smooth and creamy. Beat in the eggs, 1 at a time, until incorporated.
Add the vanilla extract and beat until incorporated, then remove the bowl from the mixer.
Sift the flour and baking powder together in a bowl, then stir into the creamed butter mixture by hand. Mix the milk into the batter until smooth.
You should have about 6 cups of batter. Pour 1 1/2 cups of the batter (or a quarter of your total batter) into one of the prepared cake pans; add a quarter of the apples and a quarter of the brown sugar mixture, lightly patting the apple mixture into the batter. Gently pour another 1 1/2 cups of the batter over the apple layer; top with another quarter of the apples and brown sugar mixture. Lightly pat the apples into the batter.
Repeat with the remaining cake pan, batter, apples and brown sugar mixture.
Bake until a toothpick inserted in the center of the cakes comes out clean, 30 to 40 minutes. Cool the cakes slightly, then invert them onto a rack to cool completely.
For the cinnamon buttercream: Add the butter, confectioners' sugar, cinnamon, vanilla and 1 tablespoon heavy cream to the bowl of a stand mixer fitted with the paddle attachment. Turn the mixer on slow to incorporate all the ingredients. If the frosting seems too thick, add the remaining tablespoon heavy cream. Turn the mixer on high and beat until the frosting is lighter and fluffier, 1 to 2 minutes. (You want the frosting to be a spreadable consistency.)
To assemble the cake: place the first layer of cake on a cake stand. Drizzle with up to 3 tablespoons of caramel. Spread the top of the layer with all of the frosting. Place the other cake layer on top and drizzle with up to 3 tablespoons of caramel. Serve immediately.
The cake keeps, covered in the refrigerator, for up to 3 days.