Preheat oven to 350°F (175°C). In a small bowl, mix 2 cups finely crushed Oreo crumbs with 1/4 cup melted unsalted butter until it resembles damp sand.
Press the Oreo mixture firmly and evenly into the bottom of a 9-inch springform pan. Bake for 8-10 minutes to set, then place on a wire rack to cool completely.
In a medium bowl, whisk together 1 1/4 cups all-purpose flour, 1/4 cup unsweetened cocoa powder, 1/2 teaspoon baking powder, 1/4 teaspoon baking soda, and 1/4 teaspoon salt. Set aside.
In a larger bowl, using an electric mixer, cream 1/2 cup softened unsalted butter and 1 cup granulated sugar until light and fluffy (2-3 minutes).
Beat in 2 large eggs one at a time, followed by 1/2 cup buttermilk, 1 teaspoon white vinegar, 1 teaspoon pure vanilla extract, and 1 tablespoon red food coloring. Mix until smooth and vividly red.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Pour the red velvet batter into a separate, greased and floured 9-inch round cake pan. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for about 15 minutes, then turn it out onto a wire rack to cool completely. Level the top with a serrated knife if needed and reserve a few crumbs for garnish.
Reduce oven temperature to 325°F (160°C). In a large bowl, beat 16 ounces room-temperature full-fat cream cheese with an electric mixer until completely smooth and lump-free.
Add 1/2 cup granulated sugar and continue to beat until creamy. Add 2 large eggs one at a time, mixing on low speed after each addition until the yolk disappears.
Finally, mix in 1/4 cup sour cream and 1 teaspoon vanilla extract on low speed, avoiding incorporating too much air.
Carefully place the cooled red velvet cake layer on top of the Oreo crust inside the springform pan. Pour the cheesecake batter evenly over the red velvet cake and smooth the top with a spatula.
Prepare a water bath: Wrap the outside of the springform pan with a few layers of heavy-duty aluminum foil. Place the wrapped pan in a larger roasting pan and fill the roasting pan with about an inch of hot water.
Place the roasting pan with the cheesecake into the preheated oven. Bake at 325°F (160°C) for 50-60 minutes, until the edges are set but the center still has a slight wobble.
Turn off the oven, crack the door open, and let the cheesecake cool inside the oven for at least an hour.
After cooling in the oven, remove the cheesecake from the water bath and let it cool on the counter to room temperature.
Cover the cheesecake with plastic wrap and refrigerate for at least 6 hours, but preferably overnight, to allow it to set completely.
For an optional white chocolate ganache drizzle: Heat 1/4 cup heavy cream until just simmering. Pour it over 1/2 cup white chocolate chips in a bowl. Let sit for 5 minutes, then stir until smooth. Let cool slightly before drizzling over the chilled cheesecake.
To serve, decorate with whipped cream, the reserved red velvet cake crumbs, and some crushed or halved Oreos.
Store any leftovers in the refrigerator, either in the springform pan covered tightly with plastic wrap or in an airtight container, for up to 5 days.