Preparation

• Adjust the oven rack to the lower-middle position and preheat oven to 350°F (177°C). Tightly wrap 1 or 2 sheets of heavy-duty aluminum foil around the bottom and sides of a 9-inch or 10-inch springform pan and set aside.
• Make the blueberry sauce first: Whisk the cornstarch, lemon juice, and warm water together in a small bowl until the cornstarch has dissolved. Set aside. Warm the blueberries and sugar together in a small saucepan over medium heat. Stir continuously for about 3 minutes, until the blueberries begin to release their juices. Add the cornstarch mixture and continue to stir for another 2–3 minutes, smashing some blueberries as you go. The mixture will begin to thicken. Remove from heat and press the mixture through a fine mesh sieve into a small bowl to separate the cooked berries from the thickened juice. Transfer the cooked blueberries to another bowl and set both aside.
• Make the crust: If you’re starting out with full graham crackers, use a food processor or blender to grind them into fine crumbs. Pour into a medium bowl and stir in the sugar until combined, and then stir in the melted butter. The mixture will be sandy. Try to smash/break up any large chunks. Pour the mixture into the prepared pan. With medium pressure using your hand, pat the crumbs down into the bottom and partly up the sides to make a compact crust.
• Bake the crust for 10 minutes. Allow to slightly cool as you prepare the filling.
• Make the filling: In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the cream cheese and granulated sugar together on medium speed until the mixture is smooth and creamy, about 3 minutes. Add the sour cream and vanilla extract and beat until fully combined. With the mixer running on low speed, add the eggs one at a time, beating after each addition until just incorporated.
• Pour the cheesecake batter into the crust and smooth the top. Drop spoonfuls of the smooth blueberry sauce onto the batter. Using a knife, gently swirl the sauce into the batter.
• Prepare the water bath: Boil a kettle of water. Place the wrapped springform pan inside of a large roasting pan. Carefully pour the hot water into the roasting pan and place it in the oven.
• Bake the cheesecake for 55–65 minutes, or until the center is almost set.
• Turn the oven off and open the oven door slightly. Let the cheesecake sit in the oven in the water bath as it cools down for 1 hour.
• After cooling, remove the cheesecake from the oven and water bath, discard the foil, and let it cool completely at room temperature. Cover and refrigerate the cheesecake for at least 6 hours or up to 2 days.
• Run a knife around the edges of the springform pan to help loosen the cheesecake, then remove the outer rim. Cut into slices for serving.
• Cover and store leftover cheesecake in the refrigerator for up to 4 days.