Preheat oven to 350°F. Grease 3- 6" round pans, and line the bottoms with parchment paper rounds, if desired. Set them aside.
In a large bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.
In a separate bowl, whisk together the brown sugar, vegetable oil, sour cream, eggs, vanilla extract, and buttermilk. Pour the wet ingredients into the dry ingredients. Whisk until everything is combined and the cake batter forms.
Pour the batter evenly between the three prepared pans. Bake the cakes for 30-32 minutes. A toothpick should come out clean. Let the cakes cool in the pans for about 10 minutes, then transfer them to a cooling rack to finish cooling completely.
Making the Apple Filling
Melt the butter in a large skillet.
Whisk the cinnamon, nutmeg, and cornstarch in a small bowl. Add in the rest of the
Cook for about 15 minutes until the mixture thickens and the apples become soft. Allow the apple filling to cool completely.
Making the Brown Sugar Buttercream
Cream together the softened butter and brown sugar for about 3 minutes.
Add in the vanilla extract, salt, and cinnamon. Then add in the powdered sugar one cup at a time. Once it's all added, mix the buttercream on medium speed for 2 minutes until light and fluffy.*
Assembling the Cake
Cut and trim the tops of all three cake layers so they're flat.
Place the first cake layer down on the cake plate. Spread on a thin layer of buttercream on top of the cake layer. Pipe a border of buttercream along the outer edge of the cake.
Spoon and spread half of the apple mixture between the buttercream edge.
Repeat the steps 1-3 with the second cake layer.
Place the 3rd cake layer on top. Coat the top and outside of the cake with the remaining buttercream. You can add swirls of buttercream on top, if desired.
Notes
*If you want your frosting thinner, add a tablespoon or two more of heavy cream. If you want it a little firmer, add up to ¼ cup more of powdered sugar.