Preheat the oven to 350°F and grease a 9-inch springform pan.
Combine the graham cracker crumbs, sugar, and melted butter in a bowl and mix until well combined. Press the mixture onto the bottom of the prepared pan and bake for 10 minutes. Remove from the oven and let it cool.
In a small bowl, mix the cornstarch and water together and set aside.
In a medium saucepan, heat the blueberries and sugar over medium-high heat until the sugar has dissolved and the blueberries have broken down, about 10 minutes. Lower the heat and add the cornstarch mixture. Stir until the mixture has thickened, about 2-3 minutes. Turn off the heat and let the mixture cool.
For the cheesecake filling, in a large bowl, beat the softened cream cheese, sugar, sour cream, and vanilla extract until smooth, about 2-3 minutes. Add eggs, one at a time, mixing well after each addition.
Pour the cheesecake filling over the cooled graham cracker base. Spoon the blueberry filling over the cheesecake filling and swirl it using a knife.
Bake the cheesecake for 45-50 minutes, or until it's set. Turn off the heat and let the cheesecake cool in the oven with the door slightly open for an hour. Remove from the oven and let it cool to room temperature for about an hour before covering with plastic wrap and chilling for at least 4 hours or overnight.
For the caramel sauce, melt the sugar and water in a saucepan over medium heat. Do not stir the mixture. Once the sugar has melted and turned dark amber in color, turn off the heat and add the heavy cream, stirring until well combined. Add the butter and stir until the sauce is smooth. Let it cool slightly before drizzling over the chilled cheesecake.