Make sure that cream cheese is at room temperature. Beat cream cheese until smooth.
I used homemade pumpkin puree. Otherwise, you can use the canned one. Add pumpkin puree, eggs, egg yolk, sour cream, sugar and the spices.
Add flour and vanilla. Beat together until well combined.
Microwave semi-sweet chocolate chips in medium uncovered microwave-safe bowl on HIGH (100%) power for 30 seconds. Stir well. The chips may retain some of their original shapes. If necessary, microwave at additional 10- to 15-second intervals, stirring just until chocolate chips are melted. Cool to room temperature.
Making marble - Remove ¾ cup pumpkin mixture. Stir into melted chocolate. .
Pour remaining pumpkin mixture into the prepared oreo crust. Spread out evenly.
Spoon chocolate-pumpkin mixture over the top. Swirl using a toothpick.
Bake the cheesecake not using the water bath- Raise the oven temperature to 450 degrees F. Place springform pan on a baking sheet (this will help catch any leaks) and bake for 15 minutes.
Turn the oven temperature down to 225 degrees F. Bake until edge is set and cheesecake is slightly jiggly in the center, 1 hour to 1 hour 15 minutes. Turn the oven off and open the door wide. The cake will not be completely set in the center. Allow the cake to sit in the oven with the door open for 30 minutes. Take the cake out of the oven and allow it to sit at room temperature for another 2 to 3 hours until completely cooled. Wrap and refrigerate overnight.
Remove the cake from the springform pan by carefully running a hot knife around the outside of the cake. Leave the cake on the bottom of the springform pan for serving.