Preheat oven to 350 degrees F. Spray and flour a 9x13 pan. Set aside.
In a medium bowl, whisk together the flour, baking soda, cinnamon, salt, nutmeg, and allspice. Set aside.
In a large bowl, whisk together the sugar, oil, eggs, and vanilla extract. Slowly stir in the flour mixture. The batter will be thick. Stir in the apples until cake batter moistens.
Pour batter into prepared pan and bake for 45 minutes or until the cake is golden brown and set. Remove from oven and cool completely on a wire cooling rack.
While the cake is cooling, make the cream cheese frosting. In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese until it is completely smooth. Add the butter and beat until combined. Add the vanilla and powdered sugar and beat until smooth, about 1 minute.
Frost the cooled the cake with cream cheese frosting. Cut into pieces and serve.
Note-The frosted cake can be keet, refrigerated and tightly covered, for up to 3 days. I like the cake chilled or at room temperature.