Preheat the oven to 350°F.
Grease and flour the bottom and sides of two 9-inch round cake pans, then line the bottoms with parchment paper.
Whisk the flour, brown sugar, baking soda, cinnamon, ginger, cardamom, black pepper, nutmeg, cloves, and salt together in a large mixing bowl.
In a separate container, such as a liquid measuring cup, stir together the milk, oil, applesauce, and vanilla.
Add the milk mixture to the bowl with the flour mixture. Stir the ingredients together until fully blended.
Divide the batter among the two prepared baking pans.
Bake the cake layers for 22 to 24 minutes, until a toothpick inserted into the center comes out clean.
Transfer the pans to a cooling rack and let the layers cool completely before removing the cakes from the pans.
Once the cake layers have cooled, invert one of the layers onto a plate. Remove the parchment paper, then spread the top with a layer of frosting. Invert the second layer onto the first layer, then spread the remaining frosting over the top and sides of the cake.
Slice and serve, or chill for later.