Begin by placing 1½ cups of Oreo cookies into a food processor and pulse until finely crushed. Combine the cookie crumbs with ½ cup of melted unsalted butter until thoroughly mixed. Press this mixture firmly into the bottom of a 9x13 inch dish, creating an even layer. Chill it in the fridge or freezer for about 15 minutes to firm up the crust.

In a mixing bowl, beat together 12 oz of room temperature brisk style cream cheese, 1½ cups of powdered sugar, 1 teaspoon of vanilla extract, and 1 teaspoon of peppermint extract until smooth and creamy. Gently fold in 1½ cups of stabilized whipped topping and ½ cup of crushed candy canes until a light pink mixture forms. Spread this peppermint cheesecake layer evenly over the chilled Oreo crust and place it in the freezer for 10-15 minutes.

In a large mixing bowl, whisk together 2 packages of chocolate pudding mix and 2¾ cups of milk for about 2 minutes until the mixture begins to thicken. Spread the chocolate pudding on top of the peppermint cheesecake layer.

After the chocolate pudding layer has set, spread the remaining 1½ cups of stabilized whipped topping over the chocolate layer evenly. Cover the dish with plastic wrap and chill it in the refrigerator for at least 5 hours.

Just before serving, sprinkle the remaining ¼ cup of crushed candy canes on top for a festive touch. Cut into squares and serve chilled.