I have had this type of dessert on several different occasions. Perhaps you have too. I couldn't find one posted that was exactly like this, and this is how I make it. I will say that it doesn't taste as good with chocolate pudding..don't know why; it seems like it should. I just don't like it that way, even tho' I am a chocoholic! Try this out and see what you think!
In a mixing bowl, cream butter and sugar and then add flour and remanning ingredients. Dough will be crumbly. Press into a 9 X 13 baking dish and bake at 350* for 15 minutes or until it starts to get golden brown around the edges. Remove from oven and set aside to cool.
2Cheese Filling Layer:
In mixing bowl, mix the bcream cheese with powdered sugar and brown sugar until smooth and creamy. Add in vanilla. Then carefully fold in whipped cream or cool whip until incorporated. Spread layer over cooled crust.
3Pudding Filling Layer:
In a mixing bowl combine all ingredients and whip them up until pretty thick. You may have to put in fridge for a couple of minutes to thicken. When it has thickened, spread this layer over the cream cheese filling.
Let sit in refrigerator to set up for a few hours.
I like to top with swirled sweetened whipped cream; but you can certainly use Cool Whip if you prefer. Garnish with shaved white chocolate, or whatever you wish. Store, covered in the refrigerator until ready to serve. Cut in squares, and serve!