Add the Oreo cookies to a food processor bowl. Cover and pulse until you have fine crumbs. Pour in the melted butter and pulse to combine. (It should resemble wet sand and hold together when pressed.)
Transfer the mixture to a 9-inch springform pan. Press the Oreo crumbs into the bottom and halfway up the sides of the pan to form the crust. Cover with plastic wrap and refrigerate while you prepare the filing.
Filling
Add the cream cheese and sugar to a large mixing bowl (or stand mixer bowl). Beat together on medium speed with a hand mixer until smooth and combined.
On low speed, mix in the sour cream. Once combined, pour in the Baileys and mix until smooth. Then mix in the instant pudding until combined.
Using a rubber spatula, fold in the Cool Whip until it's fully incorporated (no streaks). Uncover the crust and pour the filling into the springform pan. Spread it into an even layer.
Cover with plastic wrap and refrigerate the cheesecake for at least 4 hours, preferably overnight.
Chocolate Ganache
Add the chocolate chips to a medium mixing bowl. Set aside.
Pour the heavy cream and Baileys into a microwave-safe bowl. Heat in 30-second increments, stirring between each heating, until the cream is hot to the touch and steaming. (Do not bring it to a boil!)
Pour the hot cream over the chocolate chips and let sit for 5 minutes.
Whisk everything together until it's smooth and glossy. (There will be a point where the mixture looks broken, don't worry. Just keep whisking.)
Cover the cheesecake and pour the ganache all over the top in an even layer. Refrigerate for 5-10 minutes until the ganache begins to firm up. (For the pretty drip effect, save some ganache, spoon a little extra over the edges of each slice, and let it drip down.)
Release the side of the springform pan and remove it. If desired, pipe extra Cool Whip around the edge of the cheesecake and sprinkle with chocolate shavings or Oreo crumbs. Cut into 12 slices and enjoy!
Notes
If you don't have a food processor, put the Oreo cookies into a large food storage bag, press out the air, and seal it. Then use a rolling pin to crush the cookies into crumbs. Put the crumbs in a mixing bowl and mix in the butter.
If you don't have salted butter, use unsalted butter and add 1/4 teaspoon of salt to the Oreo mixture.
You'll need 1 small box of instant pudding. Use a tablespoon measuring spoon to portion out what you need. There will be extra pudding mix left over.
Store leftovers, covered, in the fridge for up to 5 days. Freeze for up to 2 months, and thaw in the fridge overnight before serving. (The ganache may harden and crack if frozen.)