In a mixing bowl, combine crushed vanilla wafer crumbs, melted unsalted butter, and sugar until it forms a moist mixture. Press this mixture firmly into the bottom of a 9 x 9-inch pan, creating an even layer. Refrigerate for about 10 minutes to help it set.

In a large bowl, beat softened cream cheese and whole milk together until smooth and creamy. Gradually add in sugar and finely crushed peppermint candy, mixing well. Gently fold in whipped topping until light and fluffy, then spread evenly over the chilled crust.

In a separate bowl, whisk together the instant chocolate pudding mix with the required amount of milk for 2 minutes until thickened. Pour the chocolate mixture over the peppermint layer.

Spread another layer of whipped topping over the chocolate layer. Sprinkle coarsely chopped peppermint candy canes on top.

Chill in the refrigerator for at least 4 hours or freeze for 1 hour before slicing into squares and serving chilled.