Preheat oven to 350°F (180°C). Spray 2 (8-inch) round cake pans with baking spray with flour. Line bottom of pans with parchment paper.

In a medium bowl, whisk together flour, cinnamon, baking powder, salt, baking soda, allspice, nutmeg, and ginger.

In a large bowl, whisk together buttermilk, applesauce, oil, and vanilla; stir in sugars. Add flour mixture, and whisk until just combined. Divide batter between prepared pans, smoothing tops.

Bake until a wooden pick inserted in center comes out with a few moist crumbs, 25 to 30 minutes. Let cool in pans for 10 minutes. Remove from pans, and let cool completely on wire racks.

Level cooled cake layers, if desired. Place 1 cake layer, cut side up, on a serving plate. Spread 11⁄2 cups (306 grams) Vanilla Bean Buttercream onto cake layer. Top with remaining cake layer. Spread remaining Vanilla Bean Buttercream on top and sides of cake, creating a slight border around top edge. Refrigerate for at least 30 minutes.

Just before serving, spoon Spiced Apple Topping on top of cake within border. Cover and refrigerate for up to 3 days.