In a medium bowl, combine the crushed chocolate sandwich cookies and the melted butter. Stir them together until the crumbs are evenly moistened. Press the mixture firmly into the bottom of a 9 by 13 inch baking dish, making sure to create an even layer. Place the dish in the refrigerator to chill while you prepare the next layer.
In a large mixing bowl, beat the softened cream cheese until it is smooth and creamy. Add the powdered sugar, alcohol-free vanilla extract, and peppermint extract, then beat again until well combined. Gently fold in half of the whipped topping (about 8 ounces) using a spatula. Spread this mixture evenly over the chilled cookie crust.
In another large bowl, whisk together the two boxes of instant chocolate pudding mix and the cold milk. Continue whisking for about two minutes until the mixture begins to thicken. Let it sit for a moment to firm up slightly, then carefully pour it over the cream cheese layer, spreading it to the edges with a spoon or offset spatula.
Spread the remaining whipped topping over the top of the chocolate pudding layer. Sprinkle the crushed candy canes and mini chocolate chips evenly over the entire surface. The bright red and white candy bits will immediately give the dish its festive holiday look.
Cover the dish loosely with plastic wrap or a lid and refrigerate for at least four hours, though overnight is even better. This allows the layers to set properly so you can cut clean, beautiful squares when it is time to serve.
