Caramel Apple Cake

1. Preheat oven to 350 degrees. Coat cake pans with cooking spray; cover bottoms with parchment, and coat again. Set aside. Sift together flour, baking soda, cinnamon, and salt in a large bowl; set aside.
2. Shred apples on a box grater. Transfer to paper towels; press gently to drain. Transfer to a medium bowl, and toss with 1/2 cup flour mixture to coat completely.
3. Put sugars and butter into the bowl of an electric mixer fitted with the paddle attachment; mix on medium-high speed until fluffy. Add eggs, 1 at a time, mixing well after each addition. Add remaining flour mixture; mix until just combined. Mix in apple butter and oil. Add shredded apples, and mix until combined. Divide batter among prepared pans.
4. Bake until a cake tester inserted into centers comes out clean. Transfer to wire racks; let cool in pans slightly. Invert cakes onto racks. Remove parchment; reinvert. Cakes can be wrapped in plastic and stored up to 1 day.

Batter amounts and cooking times for 3-inch-deep round pans

1. 6-INCH: 3 cups batter per cake (6 cups total), 1 hour; 8-INCH: 5 cups batter per cake (10 cups total), 1 hour 15 minutes; 10-INCH: 7 1/2 cups batter per cake (15 cups total), 1 hour 15 minutes.

To assemble

1. Cut each cake in half horizontally, making 4 layers of each size. Spread caramel filling on 3 layers. Stack, placing plain layer on top. Frost top and sides of each tier with buttercream.

Filling and frosting amounts for each tier

1. 6-INCH: 1/4 cup caramel filling per layer (3/4 cup total), 1 1/4 cups buttercream for exterior; 8-INCH: 1/3 cup caramel filling per layer (1 cup total), 2 cups buttercream for exterior; 10-INCH: 1/2 cup caramel filling per layer (1 1/2 cup total), 3 1/2 cups buttercream for exterior.