Using an electric mixer beat together the cream cheese, sugar, eggs, and flour in a medium bowl. Continue to beat on high until the ingredients are combined and appear smooth. Add the vanilla, mixing until blended.
Steps to make the cheesecake:
Divide the pumpkin cake batter in half. Spread the first half of the batter into the bottom of the prepared pan.
Divide the cheesecake batter in half. Dollop (using a large spoon) the first half of the cheesecake batter on top of the pumpkin cake batter. (Don't spread or swirl the cheesecake batter, just dollop.)
Slowly add the remaining the pumpkin cake batter by using spoonfuls of dollops around the cheesecake batter. Do not spread the pumpkin cake batter.
Add the remaining cheesecake batter on top of the other 3 layers. Spread this batter using an offset spatula into an even layer.
Bake at 350 degrees for 50-60 minutes.
If the cheesecake appears to be browning too fast make a foil tent to cover the top for the last 20-30 minutes.
Be aware that the cheesecake will puff up in the oven.
The cake may also crack but after it is cooled it will settle.
Remove from the oven.
Transfer the cheesecake to a wire rack to cool completely.
Next move the cooled cheesecake to the refrigerator for at least 4 hours or overnight.