Preheat the oven to 350 degrees F.
Spray a 9x13" baking dish with cooking spray.
In a large bowl, whisk together the oil, sugar, eggs, and vanilla.
Stir in the cinnamon, baking soda, nutmeg, salt, and allspice.
Add the flour and stir until combined. The batter will be thick!
Fold in the shredded apples.
Spread the cake batter into the prepared pan.
Bake in the preheated oven for 40-45 minutes. The top will be brown and the middle should be baked through.
Cool completely, about 1 hour.
In a medium bowl, beat together the cream cheese and butter until creamy.
Add the powdered sugar, vanilla, and milk.
Spread over the cooled bars.
Cut into squares.
Enjoy!