Prepare the pudding: Whisk the instant pudding mix and cold milk together in a large bowl until thickened, about 2 minutes. Set aside.
Make the cream cheese layer: In a separate bowl, beat the softened cream cheese, powdered sugar, and vanilla extract until smooth and creamy.
Fold the whipped topping into the cream cheese mixture until just combined.
Assemble the first layer: Line an 8×8 inch baking pan with plastic wrap, leaving an overhang on the sides for easy removal later. Arrange half of the brownie cubes in a single layer on the bottom of the pan.
Layer the fillings: Spread half of the cream cheese mixture evenly over the brownie layer. Top this with half of the prepared chocolate pudding.
Repeat the layers: Add the remaining brownie cubes, followed by the remaining cream cheese mixture, and finally the remaining chocolate pudding.
Chill: Cover the pan tightly with plastic wrap and refrigerate for at least 6 hours, or preferably overnight, until the cake is firm.
Serve: Use the plastic wrap overhang to lift the cake out of the pan. Slice into squares. Drizzle with chocolate syrup before serving, if desired.
Notes
You can use store-bought fudge brownies or bake your own batch ahead of time and let them cool completely.
For a richer flavor, use whole milk when preparing the pudding.
If you do not have an 8×8 pan, a 9×9 pan works, but the layers will be slightly thinner.