Make the Cake: 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 an electric mixer on medium speed, beat the butter 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 mix on low for an additional 30 seconds to combine.
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.
Make the Salted Caramel Buttercream: In a medium, heavy-bottomed saucepan, whisk the sugar and flour together. Add the milk and cream and cook over medium heat, whisking occasionally, until the mixtures comes to a boil and has thickened, about 10 to 15 minutes.
Transfer the mixture to the bowl of a standing mixer fitted with the paddle attachment. Beat on high speed until cool, about 5 minutes. Reduce the speed to low and add the butter and vanilla; mix until thoroughly incorporated. Increase the speed to medium-high and beat until the frosting is light and fluffy. (It might seem like it won't get to the fluffy point, but stick with it, it'll get there!) Add the salted caramel sauce and continue mixing until combined and fluffy. (If the frosting is too soft, put the bowl in the refrigerator to chill slightly, then beat again until it reaches a fluffy consistency.)
Assemble the Cake: If any of the cake layers have domed on top, trim the top off to create flat surfaces. Place one cake layer on a serving platter. Spread 1¼ cups of the frosting on top. Add the next layer and top with 1¼ cups 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. Refrigerate for 15 minutes, until firm. Frost the sides and top of the cake with the remaining frosting. Drizzle some additional salted caramel sauce on top and sprinkle with chopped peanuts. Return to the refrigerator for at least 15 minutes prior to serving.
The cake can be kept in an airtight cake saver (or wrapped tightly in plastic wrap) at room temperature for up to 3 days. If your kitchen is particularly warm or humid, store the cake in the refrigerator. Allow the cake to sit at room temperature for at least 2 hours before serving.Nutritional values are based on one serving