Preheat your oven to 325°F (163°C). Combine Oreo crumbs with melted butter until well mixed. Press this mixture into the bottom of a springform pan. Bake for 8 minutes and let it cool completely.

In a mixing bowl, beat softened cream cheese with granulated sugar until smooth, about 2 minutes. Gradually mix in sour cream and vanilla extract, then add eggs one at a time without overmixing. Set aside.

In a separate bowl, whisk together vegetable oil, granulated sugar, cocoa powder, buttermilk, vinegar, and vanilla extract until smooth. Gradually add flour and baking soda, whisk until combined, then add red food coloring until desired hue is achieved.

Pour half of the cheesecake filling over the cooled Oreo crust. Add dollops of the red velvet batter, followed by the remaining cheesecake filling. Use a knife to swirl together.

Bake in the oven for 55–65 minutes, until the center is slightly jiggly but set. Turn off the oven and crack the door open, letting the cheesecake cool inside for 1 hour.

Transfer the cheesecake to the refrigerator and chill for at least 4 hours or overnight.

Remove from the springform pan, top with whipped cream, festive sprinkles, and crushed Oreo cookies if desired, then serve chilled.