1. Preheat oven to 350º and position an oven rack in the middle of the oven. Make cheesecake: In a large bowl using a hand mixer or in the bowl of a stand mixer using the paddle attachment, beat cream cheese until smooth. Add pumpkin purée, eggs, sugars, sour cream, flour, pumpkin pie spice, cinnamon, and vanilla and beat until combined and no clumps remain. Set aside.
2. Make crust: In a large Ziploc bag or a food processor fitted with a metal blade, crush or blend Oreos until fine crumbs form. Transfer to a bowl and pour in melted butter. Stir until crumbs are completely coated and moist.
3. Coat a 9" springform pan with cooking spray and press Oreo mixture into pan and 1/3 of the way up the sides, packing tightly. Pour cheesecake filling over crust.
4. Bake until cheesecake is only slightly jiggly in the center, 1 hour to 1 hour 15 minutes. (If you want to use a water bath to ensure cheesecake top does not crack, wrap the outside of the pan in aluminum foil and place in a baking dish. Place on oven rack and pour in enough boiling water to reach halfway up the pan. Follow baking instructions.)
5. If using a water bath, remove pan from water and unwrap foil. Refrigerate cheesecake until totally chilled, at least 4 hours and up to overnight.
6. When ready to serve, drizzle with melted chocolate and caramel. Serve with whipped cream or Cool Whip, if desired.