Process the chocolate sandwich cookies in a food processor until fine crumbs form. Alternatively, place the cookies inside a sturdy bag and crush them finely with a meat pounder.
Pour the melted unsalted butter into the cookie crumbs and stir thoroughly until the crumbs are evenly coated.
Transfer the mixture to a 9-inch springform pan and firmly press it across the bottom in an even layer.
If the crumbs cling to your hands while pressing, cover the surface with plastic wrap and use the flat bottom of a measuring cup to compact and level the crust.
Set the prepared crust aside while making the filling.
Place the very cold heavy cream in the bowl of an electric mixer and whip until stiff peaks develop, approximately 2–3 minutes.
Transfer the whipped cream to a separate bowl and reserve it for the filling.
Using the same mixer bowl without washing it, beat the softened cream cheese for approximately 2–3 minutes, or until completely creamy and smooth.
Pour in the sweetened condensed milk and continue mixing until the filling is uniform, silky, and completely free of lumps.
Add approximately half of the reserved whipped cream to the cream cheese mixture. Fold it in gently to lighten the filling.
Add the remaining whipped cream and continue folding carefully until the mixture is evenly combined. Avoid vigorous stirring so the whipped cream retains as much volume as possible.
Fold the crushed peppermint candy into the creamy cheesecake mixture until evenly distributed.
Spoon or pour the finished filling over the prepared chocolate cookie crust and spread it evenly in the springform pan.
Cover the pan securely with plastic wrap and transfer it to the freezer. Freeze for a minimum of 8 hours, allowing the cheesecake to become completely firm.
Take the cheesecake out of the freezer approximately 20 minutes before serving so it softens slightly and is easier to slice.
Carefully cut the cheesecake into portions and serve while still chilled.