Company Spice Cake

Preheat oven to 350 degrees F and grease an 8×8 baking dish.
Mix the flour, baking powder, baking soda, salt, and spices together in a large bowl.
In a separate large bowl, beat together the eggs, sugars, and oil until smooth. Add applesauce, buttermilk, and vanilla to the mixture.
Slowly add the wet ingredients to the dry ingredients and mix until just incorporated.
Transfer the batter to the prepared baking dish and bake for 35-40 minutes or until an inserted toothpick comes out clean.
In a small bowl, mix together the icing ingredients and pour over the cake while still warm.
Let cake cool for 20 minutes, then slice and enjoy.