Combine the crushed chocolate sandwich cookies and the melted butter in a medium bowl. Stir until the crumbs are well coated. Press the mixture firmly into the bottom of a 9×13 inch baking dish to create an even layer. Place the dish in the freezer for about 10 minutes to help the crust set 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 mix until fully combined. Gently fold in half of the whipped topping (8 ounces) until the mixture is light and fluffy. Spread this peppermint cream over the chilled cookie crust in an even layer.
In another large bowl, whisk together the two packages of instant chocolate pudding mix and the 3 cups of cold milk. Continue whisking for about 2 minutes until the pudding starts to thicken. Let it sit for a moment to firm up slightly, then carefully pour it over the peppermint cream layer, smoothing it out with a spatula.
Take the remaining 8 ounces of whipped topping and spread it gently over the chocolate pudding layer. Be careful not to mix the layers, using a light touch to ensure the white topping stays clean and bright for a beautiful presentation.
Sprinkle the crushed candy canes and mini chocolate chips over the top of the dessert. Cover the dish with plastic wrap and refrigerate for at least 4 hours, though overnight is best. This allows the layers to set properly and makes it much easier to slice into neat squares before serving.
