Preheat your oven to 350 degrees F. Line a 9-inch springform pan with parchment paper and lightly spray the bottom and the sides of the springform pan with cooking spray.
Place the gingersnaps in a food processor and process them until they turn into fine crumbs. Alternatively, you can place the gingersnaps in a plastic bag and crush them using a rolling pin.
In a mixing bowl, combine the gingersnap crumbs with the granulated sugar. Mix until evenly combined.
Pour the melted unsalted butter over the gingersnap and sugar mixture. Stir well until the crumbs are evenly coated with the melted butter. Using your hands, clump the mixture together, and it should hold together. If it is too crumbly, you need more butter; if it is too wet, you need more gingersnap cookies.
Transfer the gingersnap mixture to the prepped 9-inch pan, and using the bottom of a cup or your fingers, press the mixture firmly into the bottom and up the sides of the pan to form an even crust.
Bake the crust for about 8-10 minutes. Allow it to cool completely before adding the filling. While the crust is cooling, make the cheesecake.
For the cheesecake filling:
Preheat or lower your oven to 325°F. Pour water into a sheet pan or roasting pan, filling up only a little less than halfway of the pan. Set aside.
In a large mixing bowl, using a handheld electric mixer, or in a bowl of a stand mixer fitted with the paddle attachment, beat the room temperature cream cheese on medium speed until smooth and creamy.
While the mixer is on low, gradually add the granulated sugar to the cream cheese, continuing to beat until the mixture is well combined and smooth.
With the mixer on low speed, add the pear flavoring and the room temperature egg yolk and whole eggs all at once and mix just until incorporated. With a rubber spatula, scrape the bottom and the sides of the bowl.
With a rubber spatula, gently fold in a pinch of salt. Mix the entire cheesecake filling until it is smooth, with no lumps remaining. Be careful not to overmix, as this can introduce excess air bubbles into the batter.
Carefully pour the cheesecake filling into the baked gingersnap crust. With the back of the spoon, evenly spread the cheesecake across the top. Place the cheesecake in the prepped water bath.
Bake in the oven for 35-40 minutes, bake until the middle is barely set and slightly jiggled. If the cake is still jiggling, bake for 5 more minutes.
Once the cake is done baking, let it sit for 10-15 minutes, and then place it in the fridge for at least 4 hours or overnight to set!
For the caramel sauce:
While the cheesecake is baking, make the caramel sauce.
In a medium-sized saucepan, stir together the water, sugar, and corn syrup.
On medium heat, bring the sugar to a boil. The bubbles will start off fast and small, but once it starts caramelizing, the bubbles will slow down and become a little bigger. Do not touch or stir the mixture to avoid crystallization.
Let the mixture boil until it becomes caramelized and looks golden brown. This takes a few minutes, but once it starts turning brown, it's easy to burn it, so keep an eye on it.
Put the cream in the microwave for 1 minute.
Once the caramel is golden brown and ready for the cream, turn off the heat on the sugar mixture and add the warm cream. Mix the caramel mixture until evenly combined.
Pour the mixture into a bowl. Add the vanilla, salt, and butter, and let it sit until the butter melts. Stir once the butter is melted. Let it completely cool before using.
Assembly:
Once the cheesecake is cooled and set, pour the COOLED caramel sauce on top. You can pipe whipped cream on top if you want!