Combine crushed cookies and melted butter in a medium bowl, working the mixture until it resembles wet sand. Press firmly into the bottom of a 9×13-inch baking dish, creating an even layer. Pro tip: Use the bottom of a measuring cup to compress the crumbs for a sturdier foundation.
Beat softened cream cheese and sugar until light and fluffy (approximately 2 minutes). Gradually add milk while mixing. Gently fold in 1 cup of whipped topping using a spatula with a figure-eight motion. Spread this velvety mixture evenly over the cookie base, being careful not to disturb the crumbs.
In a large bowl, whisk together pudding mixes and cold milk for 2 minutes until it begins to thicken. Pour and spread over the cream cheese layer, covering completely to the edges.
Allow the dessert to set for 5 minutes before carefully spreading the remaining 2 cups of whipped topping over the pudding layer. Sprinkle with chocolate shavings or mini chips, and drizzle with chocolate syrup in a decorative pattern.
Cover loosely with plastic wrap without touching the surface. Refrigerate for at least 4 hours, preferably overnight for the best flavor and texture.