Prepare and bake the brownies according to the package directions. Let the brownies cool completely, then cut them into bite-sized squares.
Prepare the instant chocolate pudding using 3 cups of cold milk, whisking for two minutes until thickened. Let the pudding stand for five minutes.
In a separate bowl, beat the softened cream cheese, powdered sugar, and vanilla extract until smooth and creamy. Gently fold in half of the thawed whipped topping until just combined.
To assemble the cake, use a 9×13 inch baking dish. Arrange half of the cooled brownie squares in a single layer on the bottom of the dish.
Spread the cream cheese mixture evenly over the layer of brownies.
Spoon the prepared chocolate pudding over the cream cheese layer.
Top the pudding layer with the remaining brownie squares.
Spread the remaining half of the whipped topping over the top layer of brownies.
Cover the dish tightly with plastic wrap and refrigerate for at least 6 hours, or preferably overnight, before serving.
Notes
You can use store-bought, pre-made brownies to save time.
For a richer flavor, use dark chocolate pudding mix.
If you prefer a firmer texture, use a slightly smaller amount of milk when making the pudding.