Chocolate Layer Dessert

from The Essential Mormon Cookbook (but with my own crust and other corrections)
Ingredients:
1 box shortbread cookies
¼ cup butter (melted)

8 oz. tub lite Cool Whip knock-off (thawed)
2 (8 oz.) packages cream cheese (I use 1/3 the fat Neuftchatel) (at room temperature)
2 cups powdered sugar
2 (5.9 oz.) packages chocolate instant pudding
4 cups milk
2 tsp. vanilla
a handful of chocolate chips

Directions:
Crush shortbread cookies until fine.  Stir in butter.  Press in the bottom of a 9x13 pan.  Bake at 300 for 5-8 minutes.  Cool completely.
To prepare first layer, blend together thawed Cool Whip, cream cheese and powdered sugar.  Spread over cooled crust.  Refrigerate at least 2 hours.
For the second layer, combine pudding, milk and vanilla with an electric mixer at low speed until it begins to thicken.  Spread on top of cream cheese layer and refrigerate several hours or overnight. 
Before serving, garnish with grated chocolate chips. 
To serve, cut into squares.