Preheat the oven to 350ºF. Grease two clean tuna cans and one 9x5 loaf pan. Line the sides and bottom of the tuna cans with parchment and grease again.
In the bowl of a stand mixer fitted with the paddle attachment, cream brown sugar and butter. Add the maple syrup and mix until incorporated. Add the eggs and beat well.
In a medium bowl, combine baking soda, baking powder, cinnamon, cloves, and flour.
Alternately add the dry ingredients and the applesauce to the butter mixture, mixing just until incorporated.
Pour the batter evenly into the prepared pans, filling the tuna cans about 3/4 full. Bake about 27 minutes or until a toothpick inserted in the center of a cake comes out clean. Allow the cakes to cool in the pans for 15 minutes before carefully inverting onto a wire rack to cool completely before frosting.
To make the frosting, place cream cheese in the bowl of a stand mixer fitted with the paddle attachment. Beat on low about one minute, ensuring that it is soft and pliable. Stop the mixer and scrape down the bowl. Add the butter and beat on medium speed for one minute, until thoroughly combined.
Turn the mixer on low and add the powdered sugar, followed by the vanilla extract. Beat until almost incorporated.
Stop the mixer and scrape down the bowl and beater. Beat on medium speed until the frosting is velvety soft.
To frost the cake, spread frosting on top of one of the small cakes, top with the other, and spread frosting all around the outside. Use any remaining frosting to top the loaf cake, or drizzle the loaf with vanilla glaze.