Lightly spray a 9×13-inch baking dish with nonstick spray, or line it with parchment paper.
Add the softened cream cheese, powdered sugar, and vanilla extract to a large mixing bowl. Beat until smooth and creamy.
In a separate bowl, whisk together the instant chocolate pudding mix and cold whole milk for two minutes. Let the pudding sit for three to five minutes to thicken.
Add the chocolate pudding to the cream cheese mixture and beat on low speed until smooth.
Fold in 3 cups of thawed whipped topping until the filling is light and combined.
Spread a thin layer of chocolate filling in the bottom of the prepared baking dish.
Add one layer of chocolate graham crackers over the filling, breaking crackers as needed to fit the pan.
Spread one-third of the chocolate filling over the graham crackers.
Repeat the layers two more times, ending with chocolate filling on top.
Cover the dish with plastic wrap and refrigerate for at least six hours, or overnight for the best texture.
Add the semi-sweet chocolate chips to a heat-safe bowl.
Heat the heavy cream in a small saucepan until steaming. Pour it over the chocolate chips and let it sit for two minutes.
Stir the chocolate and cream until smooth and glossy.
Let the ganache cool for about 10 minutes, then spread it over the chilled cake.
Return the cake to the refrigerator for 30 minutes, or until the ganache is set.
Garnish with the remaining whipped topping and mini chocolate chips, chocolate curls, or sprinkles if desired.
Slice and serve cold.