Drop spoonfuls of the vanilla batter and the chocolate batter into the crust, alternating between the two. Since there is more vanilla batter, make those scoops a bit larger, or add two scoops of vanilla for every scoop of chocolate.
Once all the batter is in the pan, take a butter knife and gently swirl the two mixtures together to create a soft marbled pattern.
Lightly tap the pan on the counter a few times to release any trapped air bubbles, then smooth the top.
Set the springform pan inside a 10-inch cake pan, then place that into a large roasting pan. Pour hot water into the roasting pan until it reaches about 1 inch up the sides, forming a water bath.
Bake in the preheated oven for 60 to 80 minutes. The cheesecake is ready when the edges are set while the center still has a slight wobble.
Turn off the oven and leave the door slightly open. Let the cheesecake rest in the warm oven for about 1 hour.
After that, remove it from the oven and allow it to cool at room temperature for roughly 2 hours.
Cover the cheesecake and refrigerate it for at least 6 hours, though chilling it overnight gives the best texture.
When ready to serve, run a thin knife around the edge of the pan to loosen the cheesecake, then gently release the springform ring. Slice and serve with whipped cream, fresh fruit, chocolate sauce, or any topping you like.