Preheat oven according to brownie mix directions. Grease a 9x13 inch baking pan. Prepare brownie batter following package instructions, adding 1 extra egg to the mix.
Bake brownies until a toothpick inserted comes out with moist crumbs, about 30-35 minutes. Cool completely in the pan, about 1 hour.
In a large bowl, beat softened cream cheese with powdered sugar until smooth and fluffy, about 2-3 minutes.
Gently fold in 1 container (8 oz) whipped topping until well combined. Spread evenly over cooled brownies.
In another bowl, whisk together chocolate pudding mix, vanilla pudding mix, and cold milk for 2 minutes until thickened.
Pour pudding mixture over cream cheese layer and spread carefully to cover completely.
Spread remaining 8 oz whipped topping over pudding layer, extending to the edges of the pan.
Top with chocolate shavings or drizzle with chocolate syrup. Sprinkle with mini chocolate chips if desired.
Cover tightly with plastic wrap and refrigerate for at least 4 hours, preferably overnight (8-12 hours) for best results.
Cut into squares using a sharp knife dipped in hot water. Wipe blade between cuts for clean slices. Serve cold.