• Preheat the oven to 350 °F. Line the bottom of three 8"x3" round cake pans with parchment paper.

Cake Layers

• Combine 1 ½ oz unsalted butter, ¾ oz dark rum, 6 oz light brown sugar, ¼ vanilla bean½ teaspoon ground cinnamon in a small saucepan and heat until the butter is melted and the mixture just begins to boil. Divide the warm caramel between the 3 pans. Spread the caramel in the pans, leave a 1/2" border around edges, Set aside.
• Peel core and thinly slice 24 oz apples. Divide the apple slices between the three pans, pressing into a single layer. Set the pans aside while preparing the cake batter.
• Combine 6 egg yolks, 1/2 of the sour cream and 1 tablespoon vanilla extract in a small bowl, set aside. Sift 9 oz cake flour, 1 cup (8 oz) of the sugar, ¾ teaspoon baking powder, ¾ teaspoon salt, ½ teaspoon baking soda and 4 teaspoons ground cinnamon into a mixer bowl. Mix the dry ingredients on low speed to distribute the leavening and spice.
• With the mixer running on low speed, add 9 oz unsalted butter and the remaining sour cream and mix until it forms a thick batter. Increase the speed to medium and mix about 3 minutes until the batter lightens in texture and color. Scrape the bowl and beater. With the mixer on low, add ½ the egg yolk mixture. Mix until incorporated. Add the rest of the egg yolk mixture. Mix until incorporated.
• In another bowl, Whip 3 egg whites to soft peaks. Add the remaining ¼ cup (2 oz) sugar and whip to full peak. Fold ½ the whites into the batter, then fold in the remaining whites. Divide the batter between the 3 pans and spread to an even layer.
• Bake until the center of the cake springs back when lightly pressed, about 30-35 minutes. Allow the cakes to cool for 5 minutes then turn them out while still warm onto a parchment lined sheet pan. If any caramel or apples stick in the pan scrape them out with a small spatula and place back on the cake.
• Cool, apple side up, to room temperature. Wrap and refrigerate the layers for several hours or overnight.

Maple Buttercream

• Make 1 Recipe Italian Meringue Buttercream according the to recipe, adding the maple syrup at the end of the recipe. Store at room temperature until ready to use.

Assembly

• Divide the buttercream in ½. Reserve one ½ for icing the cake, use the remaining for filling. Remove the chilled layers from the refrigerator. Unwrap and flip the cakes, apple side down, onto the plastic wrap. Use a serrated knife to trim off the crust on the top of each cake. (see note)
• Place 1 layer, apple side up, onto your serving platter. Place 1/2 of the filling onto the layer and spread it evenly to the edges. Place another layer, apple side up, onto the cake and spread the other 1/2 of the filling onto the apples. Flip the third layer onto the cake so the apples are facing down.
• Crumb coat the cake and chill until set. Ice the sides and top of the cake with the remaining buttercream. Decorate as you like. Serve at room temperature