- Position a rack in the lower third of the oven and preheat the oven to 350 degrees. Butter a 9-inch round springform pan.
- Blend together cookie crumbs and butter in a medium bowl with a fork until evenly moistened. Press the mixture evenly over the bottom of the prepared pan.
- Bake the crust for about 8 to 10 minutes until lightly golden. Let cool completely before adding the filling.
- Increase the oven temperature to 400 degrees. Place a deep baking pan in the oven to preheat; it should be large enough to hold the springform pan.
- In the bowl of a stand mixer fitted with a paddle attachment (or a large mixing bowl if using a hand-held mixer), blend the cream cheese on medium-high speed until it is smooth, for about 10 minutes. Reduce the speed of the mixer and gradually add the sugar. Cream the cheese and sugar together until light and fluffy, about 5 minutes.
- Add the eggs and yolks two at a time to the cream cheese mixture until they are fully incorporated. Scrape down the paddle and sides of the bowl. Add the sour cream, spices, vanilla bean, and vanilla extract. Mix for another 8 to 10 minutes until the filling resembles the smooth consistency of sour cream.
- Wrap the outer sides and bottom of the springform pan in heavy-duty aluminum foil, pour the filling into the cooled crust, and place the cake in the preheated deep baking pan large enough to hold it. Fill the baking pan with enough hot water to come about halfway up the sides of the springform pan.
- Bake for 10 minutes, then to turn the oven temperature down to 225 degrees and bake the cheesecake for another 1 hour and 15 minutes or until the cake is firm on the edges but still jiggles slightly in the center; it will continue to set as it cools.
- Turn the oven off and leave the cheesecake in the oven with the door partially open for 30 minutes.
- Take the cheesecake out of the water bath and allow it to cool at room temperature for 3 to 4 hours. Once it is cooled, carefully wrap the cooled cheesecake, still in the pan, in aluminum foil and refrigerate overnight.
- When ready to serve, run a hot knife around the edges of the pan to loosen the cake, then open the springform pan and release the sides. Carefully transfer the cake to a serving plate. Serve the cheesecake topped with caramel sauce.
- Have the heavy cream out close by the stove. Put 2 tablespoons of the sugar in a heavy-bottomed non-reactive saucepan and cook over medium high heat. When the sugar starts to melt around the edges (after about 2 minutes) stir the mixture gently with a heat-resistant spoon and continue to add 2 tablespoons of sugar at a time, stirring as needed before you add more.
- Continue to watch carefully as the sugar darkens to the desired caramel color. Once all the sugar is completely dissolved, remove from heat.
- Immediately add the cream slowly while stirring vigorously. If you notice lumps just return the pan to the heat and stir until it is completely smooth. Stir in the salt and let cool to warm.
- Transfer to a container and store in the refrigerator. Pull it out to reach room temperature or reheat on the stove to serve.