Using a hand mixer, mix heavy cream until you achieve soft peaks. Add in powdered sugar and vanilla, and mix until stiff peaks form, Set aside.
Line a baking dish with a layer of graham crackers. Break them into small pieces to fill in the gaps.
In a separate bowl, combine pudding mix and milk and mix well. Fold in the prepared whipped cream.
Pour 1/2 of piudding mixture over graham crackers. Place another layer of graham crackers, then pudding mix. Repeat this process once more, ending with a layer of graham crackers.
In a sauce pan, mix together butter, chocolate chips, sugar, milk, and vanilla extract. Cook for about 5 minutes over a very low simmer until smooth.
Pour over graham crackers, spreading evenly.
Cover and chill overnight. Slice and serve!