Preheat oven to 350 degrees. Spray a 13 by 9-inch baking dish with non-stick cooking spray.

In a large mixing bowl whisk together flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, and allspice for 30 seconds. Make a well in the center and set aside.

To a separate large mixing bowl add granulated sugar, brown sugar, and eggs. Using an electric hand mixer beat on medium speed until fairly pale and fluffy, about 2 minutes.

Add applesauce, vegetable oil and 1 teaspoon vanilla extract to sugar mixture and blend with hand mixer until combined.

Pour applesauce mixture into well in flour mixture then gently fold and stir mixture just until there's no longer streaks or pockets of flour. Mixture will be lumpy and that's okay.

Pour mixture into prepared baking dish. Wiggle pan to level batter out even.

Bake in preheated oven until toothpick inserted into center comes out free of batter (a moist crumb or two is fine), about 30 to 40 minutes.

Let cake cool on a wire rack (to speed up cooling you can cool in the fridge).

To make the cream cheese frosting: Add cream cheese, butter, powdered sugar and vanilla to a large mixing bowl.

Using an electric hand mixer (with clean beater blades), blend mixture on low speed until combined. Then increase speed to high and whip for several minutes until light and fluffy.

If needed you can freeze the frosting in 3 minute increments, stirring between intervals, until it's firmed up some.

Frost cake with cream cheese frosting then cut into slices.