Preheat the oven to 325°F.
Combine the Oreo cookie crumbs and melted butter in a mixing bowl. Press the mixture firmly into the bottom of a 9-inch springform pan. Bake the crust for 10 minutes, then set aside to cool.
In a large bowl, beat the cream cheese and sugar together until smooth and creamy.
Add the Baileys Irish Cream, cornstarch, and vanilla extract. Mix until well combined.
Add the eggs one at a time, mixing gently after each addition until just combined. Pour the filling over the prepared crust.
Wrap the springform pan tightly in tin foil and place in a water bath in the oven. Bake at 325 degrees for 1 hour and 10 minutes.
Turn off the oven and let the cheesecake cool inside the oven with the door slightly ajar for 1 hour. The cheesecake is done when the edges are set, and the center is slightly jiggly. It will firm up as it cools.
Heat the heavy cream and irish cream in a small saucepan until just simmering.
Pour the hot cream over the chopped chocolate and let sit for 1-2 minutes. Stir until smooth.
Pour the ganache over the cheesecake, spreading it evenly. Refrigerate the cheesecake for at least 4 hours or overnight to set completely.