Preheat oven to 350 degrees. Spray a 9x13 baking dish with non-stick spray.
Add the eggs, sugar, oil, and vanilla to a large mixing bowl and beat together on medium speed until smooth and creamy. Stir in the pumpkin.
Add the flour, pumpkin pie spice, baking powder, baking soda, and salt to the bowl and beat together until well combined.
Pour batter into prepared baking dish and bake for 35-40 minutes or until a tester comes out clean.
Cool cake completely before frosting.
For the frosting
To make the frosting, add the cream cheese, butter, vanilla, and powdered sugar to a large mixing bowl and beat on medium speed until smooth and creamy.