Preheat the oven to 350ºF (177ºC). Prepare three 6-inch cake pans or two 8-inch cake pans by spraying the sides with baking spray and lining the bottoms with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, allspice, ginger, nutmeg, and cloves. Set aside.
In a large bowl, add the brown sugar, vegetable oil, and unsweetened applesauce. Whisk together until uniform, then whisk in the eggs one at a time followed by the vanilla.
Whisk in half of the dry ingredients, followed by all of the buttermilk, then the rest of the dry ingredients. The batter will be fairly thin.
Pour the batter evenly between the prepared cake pans and bake for 32-36 minutes, until a toothpick inserted comes out clean or with just a few moist crumbs. Let the cakes cool in the pan for five minutes before turning them out onto a wire rack for an additional few hours of cooling.