Preheat your oven to 350°F (175°C). Combine crushed Oreo cookies, melted salted butter, and granulated sugar in a medium bowl. Press mixture firmly into an 8-inch springform pan and bake for 12-14 minutes. Allow to cool.

Melt the chocolate in a microwave-safe bowl or double boiler, stirring every 30 seconds until smooth. Set aside to cool slightly.

In a large bowl, beat cream cheese, granulated sugar, and cornstarch until creamy. Gradually add eggs, mixing on low speed. Blend in sour cream and vanilla until smooth.

Reserve 2 cups of filling in a separate bowl and fold in melted chocolate. In the springform pan, alternate spoonfuls of plain batter and chocolate mixture. Swirl the batters with a knife to create marbling.

Lower oven temperature to 300°F (150°C) and bake for 15 minutes. Reduce to 225°F (110°C) and bake for an additional 2 hours until edges are set.

Turn off the oven and crack the door slightly, allowing cheesecake to cool in the oven for 1 hour. Let sit at room temperature for another 2 hours before chilling for 3-4 hours or overnight.