Add the apple cider to a large sauce pan. Bring it to a simmer over medium low heat, then simmer for 45-60 minutes until reduced to ¾ cup (180 ml). Let the apple cider reduction cool completely before using.

Add the diced apple pieces, spices, brown sugar, and cornstarch to a large pan. Stir to coat the apples, then let sit for 10 minutes to allow the apples to form a juice. Cook over medium heat for about 10 minutes, stirring often. Let the apples cool completely.

Add the butter, brown sugar, flour, spices, and salt to a medium bowl. Mix everything together with your fingers until you have thick, coarse crumbs. Pop the streusel in the fridge while working on the rest of the cheesecake.

Preheat the oven to 350° F (175° C). Prepare your 9-inch springform pan for its later water bath by wrapping the bottom and sides with tinfoil. Lightly grease the pan, and line the bottom with a circle of parchment paper.

Pulse the gingersnap cookies together in a food processor until they are finely ground. Then add in the melted butter and pulse until combined. Press the cookie crumbs into the bottom and up the sides of the pan. Bake the crust for 10 minutes and then let it cool completely.

In the bowl of a stand mixer, mix the cream cheese, brown sugar and cornstarch together with a paddle attachment for two minutes on medium speed until everything is smooth. Add in the sour cream, vanilla, apple cider reduction, and spices. Mix for 1 minute on medium speed.

Next add in the eggs and egg yolks one at a time to the cheesecake batter. Mix on low speed, ensuring that each is fully mixed in before adding the next. Pour half the batter into the prepared pan with the crust, then add half of the spiced apples over the batter. Pour the remaining cheesecake batter on top, smoothing it out. Add the remaining spiced apples on top in an even layer. Sprinkle the chilled streusel over the top.

Place the cheesecake in a large roasting pan in the oven. Slowly pour the boiling water into the pan around the cheesecake. Bake at 350° F (175° C) for 1 hour and 30 minutes. When 1.5 hours are up, turn the oven off and crack the oven door open. Let the cheesecake stay in the oven for 1 more hour.

Once the 2 hours and 30 minutes are up, remove the cheesecake from the oven and let it cool completely on the counter, then refrigerate until completely cold, 8 hours or overnight.

For the Apple Cider Caramel, add the brown sugar and butter to a medium saucepan. Bring to a simmer over medium heat and let simmer for 3-4 minutes. Reduce to medium-low heat and whisk in the cream. Remove from the heat, then mix in the vanilla, apple cider reduction, and salt.

Remove the cheesecake from the springform pan and transfer it to a serving plate. Decorate as you wish, and drizzle apple cider caramel over the top. Serve each slice with extra caramel.