Preheat oven to 325 degrees F. Grease three 8-inch round cake pans, line the bottoms with a round of parchment paper, grease the parchment, then flour the pans, tapping out any excess.
In a large bowl, sift together the flour, baking soda, baking powder, salt, cinnamon, allspice and cloves.
Using a stand mixer fitted with a paddle attachment beat the butter on medium speed until creamy, about 4 minutes. Add the sugar and beat until light and fluffy, about 3 minutes. Add the eggs and beat until combined.
Reduce the mixer speed to low and add the flour mixture to the mixer bowl in three parts, alternating with the applesauce, beginning and ending with the flour mixture. Scrape down the sides and bottom of the bowl and fold in shredded apple until well combined. (Don't overmix)
Divide the batter evenly among the prepared pans and smooth the tops. Bake until a toothpick inserted into the center of the cake comes out clean, 45 to 55 minutes, rotating the pans halfway through the baking time. Transfer the pans to a wire rack and cool for 20 minutes. Turn the cakes out onto the rack, remove the parchment, and allow to cool completely.
Trim the top off to create flat surfaces. Place one cake layer on a serving platter. Spread ⅓ of the frosting on top. Add the next layer and top with another ⅓ of the frosting. Add the third layer on top and spread a very thin layer of frosting over the sides and top of the cake. I wanted mine to look more "naked" but you can adjust as you like. Decorate the top of the cake with mini apples or a drizzle of additional butterscotch sauce, if desired.
The cake can be kept in an airtight cake stand at room temperature for up to 3 days.
For the Bourbon Butterscotch Buttercream
Whisk Butterscotch Sauce, sugars and egg whites together in a steel bowl. Over medium heat, simmer a couple inches of water in a similarly sized pot. Make sure that your bowl fits well over the top and doesn't touch the water. Continuously whisk the mixture until the sugars have dissolved and everything is well combined. Transfer to the fridge and chill in the freezer for 15-20 minutes until it is cooled.
Meanwhile, beat the butter in a mixer for 2 minutes on high until it is lighter in color and fluffy. Add in the cooled syrup in two additions, beating 1 minute after each addition. Add the vanilla and bourbon beat 30 seconds until smooth.