Place the Oreos in a food processor, process them until they are fine crumbs. Drizzle in the melted butter while pulsing. Give it a stir with a spatula to make sure the crumbs are coated in the butter. Press the crumbs into a 9-inch springform pan on the bottom and slightly up the sides. Place it in the freezer while you assemble the filling.
In a large bowl, whip the cream cheese with an electric hand mixer, until smooth. Add the granulated sugar and mix it in. Add in the powdered sugar, vanilla, and peppermint extract, mix to combine, set aside.
In a medium bowl, whip the heavy cream to stiff peaks, make sure not to over-mix. Fold the whipped cream into the cream cheese mixture gently until there are no streaks. Taste and add more peppermint extract if you want more of a mint flavor.
Fold in the crushed candy canes. Divide the mixture into two bowls. Color one of the bowl with red food coloring until you get a shade of pink that you like.
Dollop the filling into the crust, so it has a mix of pink and white filling throughout, smooth out the top. Cover and place in the fridge for at least 8 hours or overnight if you can.
Take off the outer attachment of the pan, slice, and serve with toppings or as is.
Add your favorite toppings like whipped cream and more crushed candy canes.