Start by placing your chocolate sandwich cookies into a food processor and pulsing until they become fine crumbs. Transfer the crumbs to a medium bowl and stir in the melted butter until the mixture looks like wet sand. Press this mixture firmly into the bottom of a 9 by 13 inch baking dish, making sure to spread it evenly into the corners. 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 completely smooth and free of lumps. Add the granulated sugar, two tablespoons of milk, and the alcohol-free peppermint extract, then mix until well combined. Gently fold in about 1 and a half cups of the whipped topping. Spread this creamy mint layer over the chilled cookie crust using a spatula, being careful not to disturb the crumbs beneath.
In another large bowl, whisk together the two boxes of instant chocolate pudding mix with 3 and a quarter cups of cold milk. Continue whisking for about two minutes until the mixture begins to thicken significantly. Carefully spread the chocolate pudding over the cream cheese layer. Let the dish sit for about five minutes to allow the pudding to set completely.
Spread the remaining whipped topping over the pudding layer in an even, fluffy coat. Sprinkle the crushed candy canes and mini chocolate chips over the top to create a festive look. For the best results, cover the dish and refrigerate for at least four hours, or even overnight, to let the layers firm up and the flavors meld together.
