Preheat your oven to 350 degrees Fahrenheit. Combine the crushed chocolate sandwich cookies with the melted butter in a medium bowl until the mixture resembles wet sand. Press the mixture firmly into the bottom of a 9 by 13 inch baking dish. Bake for 8 minutes to set the crust, then remove from the oven and let it cool completely before adding the layers.
In a large mixing bowl, beat the softened cream cheese until smooth and fluffy. Add the powdered sugar, alcohol-free vanilla extract, and peppermint extract, then mix until fully combined. Gently fold in 8 ounces of the whipped topping. Spread this creamy mixture evenly over the cooled cookie crust using a spatula.
In another large bowl, whisk together the two packages of instant chocolate pudding mix and the 3 cups of cold milk. Whisk for about 2 minutes until the pudding starts to thicken. Let it sit for a moment to firm up slightly, then carefully pour and spread the pudding over the peppermint cream layer.
Spread the remaining 8 ounces of whipped topping over the chocolate pudding layer. Use the back of a spoon to create pretty swirls in the topping. Sprinkle the crushed candy canes and mini chocolate chips over the top to give it a beautiful, festive finish.
Cover the dish with plastic wrap and refrigerate for at least 4 hours, though overnight is even better. This chilling time allows the layers to set properly so you can cut clean, beautiful squares. Serve cold directly from the refrigerator.