Preheat the oven to 350 degrees F.
In a large mixing bowl, combine the cream cheese, sugar, and cornstarch, mixing on medium speed until smooth.
Add the eggs, one at a time, stopping to scrape the sides and bottom of the bowl with a silicone spatula after each addition.
Mix in the egg yolk, cream, and vanilla.
Whisk the cocoa powder and water together in a medium bowl, and add about half the cheesecake batter to the mixture, stirring until blended.
Add the pumpkin, cinnamon, ginger, and cloves to the remaining cheesecake batter, and pour over the prepared crust.
Drop dollops of the chocolate cheesecake batter over the top and swirl together with a toothpick.
Place the cheesecake pan into a larger baking dish, and pour water into the larger baking dish until it comes about 1 1/2 inches up the sides of the cheesecake pan.
Bake the cheesecake for 20 minutes at 350 degrees F, then turn the oven temperature down to 250 degrees F and continue to bake for about 80 minutes more, or until the cheesecake is set around the edges but still a little wobbly towards the center.
Turn the oven off, open the door slightly, and allow the cheesecake to come to room temperature.
Chill the cheesecake for at least 2 hours before slicing.