Preheat your oven to 350 degrees F (175 degrees C). Grease and flour a 9×13 inch baking pan.
In a medium bowl, whisk together the flour, baking soda, cinnamon, nutmeg, cloves, and salt. Set aside.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the eggs one at a time, mixing well after each addition.
Stir in the applesauce and vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry mixture. Mix until just combined; do not overmix.
Pour the batter into the prepared pan.
Bake for 30 to 35 minutes, or until a wooden pick inserted into the center comes out clean. Let the cake cool completely in the pan.
To make the frosting: Beat the cream cheese and butter together until smooth. Gradually add the powdered sugar, cinnamon, and vanilla extract. Beat until light and spreadable.
Spread the frosting over the cooled cake, or serve the cake dusted with powdered sugar.
Notes
This cake uses unsweetened applesauce for moisture and flavor.
For a simpler topping, dust the cooled cake with powdered sugar mixed with extra cinnamon.
This cake pairs well with a cup of hot tea or coffee.