Twist apart Oreo cookies, scrape out the white filling. Discard filling and place cookie shells in the basin of a food processor. Pulse until you have fine crumbs with no large pieces remaining.
Pour cookies into a large mixing bowl and add melted butter. Stir to combine until all crumbs are moistened.
Pour mixture into a 9” springform pan and firmly press in an even layer into the bottom and up the sides of the pan. Set aside while you prepare the filling.
Preheat oven to 325F (160C).
Place finely chopped white chocolate in a microwave-safe dish and heat in 20-second increments, stirring in between, until chocolate is smooth and melted. Set aside to cool.
In another large mixing bowl (or in the bowl of a stand mixer fitted with paddle attachment), combine softened cream cheese and sugar and beat on medium speed until smooth and creamy (don’t over-beat). Scrape down the sides and bottom of the bowl to ensure all ingredients are well-combined.
Add sour cream, vanilla extract, and peppermint extract and stir until completely combined.
Stir your white chocolate, it should not have begun to re-solidify but should not be very hot. Drizzle this into your cream cheese mixture and stir until smooth and combined.
With mixer on low-speed, add eggs and stir until just combined. Be sure to scrape the sides and bottom of the bowl to ensure everything is completely incorporated and batter is uniform, but don’t over-mix.
Add mini chocolate chips and crushed candy cane pieces and use a spatula to stir until combined.
Pour batter into prepared crust and transfer to center rack of 325F (160C) oven. Bake for 45-50 minutes or until edges are set. Center may still be slightly jiggly but should be mostly set and not liquidy.
Allow cheesecake to cool to room temperature before transferring to the refrigerator to chill for at least 6 hours before adding ganache.
Place chopped chocolate in a heatproof bowl.
Pour cream into a small saucepan over medium/low heat. Heat the cream, stirring occasionally, until it begins to steam or just begins to simmer.
Remove from heat and pour cream over chocolate (do not stir). Cover with foil and allow to sit undisturbed for 5 minutes.
Remove foil and whisk until smooth.
Pour over chilled cheesecake.
Return cheesecake to refrigerator to allow ganache to become firm. Top with crushed candy canes (note that they will begin to melt after a few hours, so sometimes I add just before serving) and whipped cream, if desired, before serving.