Keep the oven preheated to 350°. In the bowl of a stand mixer fitted with a paddle attachment combine cream cheese and sugar. Mix until smooth.
Add in vanilla and mix to combine, then add heavy cream and continue mixing until combined. Add eggs and mix for 30 seconds.
Next add in cornstarch, cinnamon, salt, nutmeg, ginger and cloves and mix until just combined.
Divide the batter in half, putting one half into a separate mixing bowl.
Add the pumpkin puree to one of the bowls and mix to combine.
Dollop the batter on top of the prebaked crust, starting with the plain cheesecake, then the pumpkin cheesecake.
Keep going back and forth until all the batter is used, then swirl the batters together with a knife.
Place into the preheated oven on the center rack. Bake for 45 minutes, until the center is set. Once baked, remove from the oven and place onto a wire cooling rack to let cool completely.
Once cooled, cover with plastic wrap and place into the fridge to let chill for 6-8 hours before serving.