Whisk pudding mix with cold milk until thick; let set 2 minutes
Beat cream cheese until smooth, then mix in vanilla
Fold pudding into cream cheese, then gently fold in whipped topping
Layer graham crackers in a 9x13-inch dish
Spread half of the cream filling over crackers
Add another cracker layer, then remaining cream filling
Finish with a final layer of graham crackers
Heat heavy cream until steaming, remove from heat, add chocolate chips and butter, stir until smooth
Pour chocolate topping evenly over the top
Cover and refrigerate at least 6 hours, preferably overnight