Preheat oven per brownie mix directions. Prepare brownie mix with package ingredients plus 1 additional egg. Bake in greased 9x13 pan until set. Cool completely in pan.
In large bowl, beat cream cheese and powdered sugar until smooth and creamy, about 2 minutes.
Gently fold in 1 container whipped topping into cream cheese mixture, preserving air bubbles. Spread evenly over cooled brownie base.
In separate bowl, whisk both pudding mixes with cold milk for 2 minutes until thickened. Let sit 5 minutes to thicken further.
Pour chocolate pudding mixture over cream cheese layer and spread evenly. Refrigerate for 15 minutes to set slightly.
Spread remaining whipped topping over pudding layer. Top with chocolate shavings or drizzle with chocolate syrup.
Cover tightly with plastic wrap and refrigerate at least 4 hours or preferably overnight before slicing. Cut with hot knife for clean edges.