Chop the chocolate into very fine pieces and place in a heatproof bowl.
Add the cream and Kahlua to a liquid measuring cup and heat in the microwave until almost boiling (this could also be done in a double boiler).
Pour the hot cream and Kahlua mixture over the chopped chocolate. Let sit for 3 minutes, then whisk until smooth. If there are still lumps of chocolate, microwave for 30 seconds on medium power (not high power, which is often the default) and whisk until smooth.
Remove the cheesecake from the oven. Remove the foil. Gently trace around the outside of the cheesecake with a thin knife and unclamp the outer ring of the springform pan. If there is condensation on top of the cheesecake, gently blot it off with a paper towel.
Pour the chocolate ganache over the top and spread into a smooth layer. It's totally ok if it drips over the sides.
Return to the fridge until ready to serve.
When ready to serve, slice with a thin, sharp knife (do not use a table knife). Be sure to slice all the way through the Oreo crust. For clean cuts, wipe off the knife in between each slice.