Preheat your oven to 350°F and pulse the Oreos in a food processor until they turn into fine crumbs. Drizzle in the melted butter while pulsing so everything clumps together evenly. Press the mixture firmly into your springform pan using a flat-bottomed glass, then bake for about 10 minutes.
Beat the room-temperature cream cheese, sugar, and salt together until completely smooth, then sift in the flour. Add the sour cream and vanilla, followed by the eggs and yolk one at a time, mixing gently after each addition. Fold in the crushed Oreos last, scraping the bowl so nothing hides at the bottom.
Pour a third of the batter into the crust, sprinkle in some chopped Oreos, then repeat this layering two more times. Bake at 350°F for 10 minutes, then lower the temperature to 300°F and continue baking for about 50 more minutes. The edges should look set while the center still jiggles slightly.
Turn off the oven but leave the cheesecake inside with the door shut for 30 minutes to prevent sudden temperature shock. Afterward, remove it and let it cool completely on the counter before covering and chilling. I always chill mine overnight for the cleanest slices.
Melt the white and dark chocolate separately with their portions of heavy cream until smooth and glossy. Pour the white ganache over the chilled cheesecake first, spreading it close to the edges. Drop spoonfuls of the dark ganache on top and swirl gently with a skewer for a marbled look.
Beat the cold heavy cream, powdered sugar, and vanilla together until soft peaks form, using a chilled bowl for the fastest results. Transfer the whipped cream into a piping bag fitted with a star tip. Pipe a corkscrew border around the edge and tuck in the halved Oreos for garnish.