Make the batter: Preheat oven to 350 degrees F. Using a small brush, lightly coat three 9-inch cake pans with softened butter or vegetable-oil cooking spray. Dust with flour and tap out any excess. Set aside.
In a medium bowl, combine the flour, baking soda, baking powder, cinnamon, nutmeg, and cloves. Set aside.
In a large bowl, using a mixer set at medium-high speed, beat the butter for 1 minute. Add the sugar and continue to beat until blended. Add the eggs and vanilla and beat for 2 more minutes. Reduce speed to low and add the flour mixture by thirds, alternating it with the applesauce and ending with the dry ingredients.
Bake the cake: Divide the batter equally among the pans and spread evenly. Bake on the middle rack of the oven until a tester inserted in the center of each cake layer comes out clean — 35 to 40 minutes. Cool in the cake pans on a wire rack to room temperature. Using a knife, loosen the cake layers from the sides of the pans and invert the layers onto the wire rack.
Finish the cake: Place one cake layer on a cake plate or stand. Spread half of the Cinnamon Whipped Cream on the layer. Place a second layer over the first and repeat. Top with the final layer and sprinkle with confectioners’ sugar, if desired, and serve. Store refrigerated for up to 4 days.