Combine the blueberries, sugar, and lemon juice in a small saucepan over medium heat. Cook for 5-7 minutes until the berries burst.
Whisk the cornstarch and water together, pour into the saucepan, and cook for 1-2 minutes until thickened. Strain through a fine mesh sieve and cool completely.
Preheat the oven to 325°F (163°C). Wrap the outside of a 9-inch springform pan with two layers of heavy duty aluminum foil.
Stir together the graham cracker crumbs, melted butter, sugar, and salt. Press firmly into the bottom of the prepared pan.
Bake the crust for 10 minutes, then set aside to cool slightly. Leave the oven on.
Beat the softened cream cheese in a stand mixer until smooth. Add the sugar and beat until creamy.
Add the sour cream and vanilla, mixing on low just until incorporated. Add the eggs one at a time, mixing on low after each. Sprinkle in the flour and mix briefly.
Pour two-thirds of the batter over the cooled crust. Drop half of the cooled blueberry sauce over it in spoonfuls. Top with the remaining batter, then the rest of the sauce.
Drag a skewer through the sauce in wide, gentle loops to create a marbled pattern. Do not overmix.
Place the wrapped springform pan inside a large roasting pan. Carefully pour hot water into the roasting pan to come 1 inch up the sides of the springform pan.
Bake for 60-70 minutes until the edges look set and the center jiggles slightly. The internal temperature should be 150°F to 155°F (65°C to 68°C).
Turn off the oven, crack the door, and let the cheesecake cool inside for 1 hour to prevent cracking.
Remove the cheesecake from the water bath and foil. Run a knife around the edge, then cool completely on a wire rack.
Cover and refrigerate for at least 6 hours, preferably overnight. Release the springform sides and serve cold with a warm, dry knife.