Combine the Oreo baking crumbs and melted butter until moistened and crumbly.
Press the mixture into the bottom of a 9-inch springform pan and refrigerate to set.
Combine the cream cheese and powdered sugar in a large bowl, mixing with a hand mixer on medium speed (or in your stand mixer) until smooth.
Add the Bailey's and mix well until incorporated.
Add the melted white and semi sweet chocolate in a steady stream while the mixer is running on low speed, until completely incorporated. Scrape down the sides of the bowl to be sure everything is incorporated.
Fold in the whipped cream or whipped topping by hand until the mixture is fluffy and creamy and there are no streaks of white in the batter.
Pour the cheesecake mixture into the prepared crust and smooth out the top with a rubber spatula.
Refrigerate to set for 6 hours or overnight, or set in the fridge for 2-3 hours and then in the freezer for 2-3 hours before serving. OR, set in the freezer only for 4 hours.
Melt the semi-sweet chocolate in the microwave on 50 percent power for 30-second increments until melted.
Whisk in the 3/4 cup plus 2 teaspoons of heavy cream until a ganache forms.
Drizzle the ganache over the chilled cheesecake.
Top with whipped cream and chocolate shavings, and serve.
Make this cheesecake up to 2 days ahead of serving. Simply store in the fridge in an airtight container.