Preheat the oven to 350℉/180℃ and line a 9" springform pan with parchment paper. Gently grease the pan, then line the bottom and sides.
Pulverize the Oreos (including the filling) until a very fine crumb forms, then combine with the melted butter and salt and combine with a fork until fully moistened.
Press the mixture into the springform pan, going at least halfway up the sides. A ⅓ cup dry measuring cup is a great tool for this. Be sure to compact it tightly into the bottom, corners, and sides.
Bake the crust for 10 minutes, then use the ⅓ cup measuring cup to re-compact the crust as it will fall slightly during baking. Cool while you make the cheesecake layer.
Reduce the oven temperature to 300℉/150℃.
Add the cream cheese to the bowl of a stand mixer fitted with the paddle attachment and mix on low speed until broken down. Scrape down the sides.
Mix together the sugar and cornstarch in a bowl, then add it to the cream cheese and mix on low until incorporated. Scrape down the sides again.
Whisk together the eggs and vanilla, then drizzle it into the cream cheese mixture (with the mixer running on low speed) in four batches until fully incorporated.
Scrape down the sides once more, then add the sour cream and mix on low speed until combined.
Add half of the cheesecake batter to another bowl and set it aside.
Chop the chocolate and add it to a heatproof bowl. Microwave the chocolate in thirty second bursts, stirring in between each round, until fully melted. Allow it to cool for about 5 minutes.
Add the melted chocolate to one bowl of batter and use a rubber spatula to fold it in until the chocolate is fully incorporated into a smooth, chocolate batter.
Use a large cookie or ice cream scoop (or large spoon) and alternate adding the chocolate and vanilla batters into the crust until they are completely used up.
Gently jiggle and tap the pan to settle the batter, then use a butter knife to make swirls throughout the batter. Be sure to get down to the crust, without breaking through the crust.
Add a 9x13" pan to the bottom oven rack and fill it with boiling water.
Carefully place the marbled cheesecake onto the center rack, then bake for 1 hour 45 minutes.
Turn off the oven, crack open the oven door, and allow it to slowly cool for one hour.
Transfer the baked cheesecake to the refrigerator (uncovered) and chill for at least 8 hours to full set and cool.
