Preheat oven to 350 degrees. Grease and flour a 9 x 13 inch baking pan.

In a large bowl, whisk together the flour, sugar, baking soda, and salt.

Stir in the vanilla, then whisk in the eggs until well combined. Stir in the crushed pineapple.

Spread the batter evenly over the prepared pan and bake for 25-30 minutes, or until a toothpick inserted in the center of the cake comes out clean. Cool before adding the topping.

In a bowl, whisk together the pudding mix and 1 1/2 cups milk until thickened and creamy, about 2 minutes.

In another bowl, beat the cream cheese and remaining 2 Tablespoons of milk until the mixture is smooth and very creamy. Add the cream cheese mixture to the pudding and stir until combined. Stir in the drained pineapple. Spread the mixture over top of the cooled cake, then spread the whipped topping over the pudding.

Chill the cake at least two hours. It will keep for several days (and is actually really excellent the second day). I prefer to serve this cake chilled.