Crush the Oreo cookies into fine crumbs and mix with the melted butter until fully coated. Press firmly and evenly into the bottom of a 9x13-inch baking dish.
Beat the room-temperature cream cheese and powdered sugar until completely smooth, about 2 minutes. Add the peppermint extract and beat briefly to combine.
Fold in one tub of thawed Cool Whip by hand until no white streaks remain. Spread the mixture evenly over the chilled crust.
Whisk the instant pudding mix with the cold milk for about 2 minutes until thickened. Let sit for 5 minutes to fully set.
Pour and spread the thickened pudding evenly over the cream cheese layer. Cover with plastic wrap pressed directly onto the pudding surface.
Refrigerate for at least 4 hours, preferably overnight, until all layers are fully set.
Just before serving, spread the second tub of Cool Whip over the pudding layer. Top with crushed candy canes, M&Ms, and reserved Oreo crumbs.
Slice with a sharp knife dipped in warm water, wiping the blade clean between cuts, and serve cold.