In a medium bowl, combine the vanilla wafer crumbs, melted unsalted butter, and 2 tablespoons of sugar. Mix until well combined and the crumbs are evenly coated. Press the mixture firmly into the bottom of a 9 x 9-inch pan, creating an even layer. Chill in the refrigerator for about 20 minutes, or until set and firm.

While the crust is chilling, use an electric mixer to beat the softened cream cheese and 2 tablespoons of milk until smooth and creamy, about 2 minutes. Gradually add in the ⅓ cup sugar and finely crushed peppermint, mixing until fully incorporated. Gently fold in 1 ¼ cups of whipped topping until just combined. Spread this delightful peppermint layer evenly over the chilled crust.

In a separate bowl, whisk together the instant chocolate pudding mix and 1 ¾ cups of milk for about 2 minutes, or until the mixture thickens to a pudding-like consistency. Carefully spread the chocolate pudding layer over the peppermint layer, ensuring an even distribution. Allow it to sit for about 5-10 minutes, allowing it to set slightly.

Take the remaining whipped topping and spread it over the chocolate layer, creating a smooth and fluffy finish. For a festive touch, sprinkle coarsely chopped peppermint candy cane over the top, allowing the vibrant colors to pop against the layers below.

Cover the pan with plastic wrap or a lid, and refrigerate the Easy No-Bake Chocolate Peppermint Squares for at least 4 hours.