Prepare the Oven: Preheat the oven to 350°F.
Make the Graham Crumbs: Break the graham crackers into pieces and process them in a blender or food processor until they become fine crumbs.
Mix the Crust: Combine the graham cracker crumbs, melted butter, and granulated sugar until evenly mixed.
Shape the Crust: Press the crumb mixture firmly across the bottom and slightly up the sides of a greased 9-inch springform pan.
Wrap the Pan: Cover the bottom and sides of the springform pan with aluminum foil, extending the foil over the top edges to help prevent water from entering during the water-bath bake.
Bake the Crust: Bake the crust for 8–10 minutes at 350°F, then allow it to cool while preparing the blueberry sauce and cheesecake filling.
Cook the Blueberries: Combine the fresh blueberries and sugar in a small saucepan over medium heat.
Prepare the Cornstarch Mixture: In a small bowl, stir together the lemon juice, cornstarch, and warm water until combined.
Thicken the Sauce: Add the cornstarch mixture to the blueberries, stirring while gently crushing some of the berries. Continue until the mixture begins to thicken, then remove the saucepan from the heat.
Strain the Blueberry Mixture: Pass the cooked blueberry mixture through a fine-mesh strainer, separating the blueberry juice from the cooked berries. Reserve both separately for later.
Smooth the Cream Cheese: Beat the softened cream cheese in a stand mixer until smooth.
Add the Sugar: Add the granulated sugar and beat for 2–3 minutes until incorporated.
Add the Sour Cream: Mix in the sour cream and vanilla extract until combined.
Blend in the Eggs: Add the room-temperature eggs one at a time, mixing after each addition only until each egg is just blended into the filling.
Fill the Crust: Pour the cheesecake filling over the cooled graham cracker crust and spread it evenly.
Add the Blueberry Swirl: Spoon about ¼ cup of the strained blueberry sauce over the cheesecake batter, keeping the cooked berries out of this step.
Reserve the Berry Topping: Stir the remaining blueberry sauce back into the reserved cooked berries and set the mixture aside for serving later.
Create the Marble Effect: Use a knife to gently swirl the blueberry sauce through the surface of the cheesecake, creating a marbled pattern.
Prepare the Water Bath: Place the foil-wrapped springform pan inside a large roasting pan or deep baking sheet filled with ½–1 inch of hot water.
Bake the Cheesecake: Bake for 55–65 minutes, until the cheesecake is almost set but the center still has a couple of inches that remain slightly unset.
Rest in the Oven: Turn off the oven, open the oven door slightly, and leave the cheesecake inside for 1 hour.
Cool Completely: Remove the cheesecake from the oven and allow it to cool to room temperature.
Chill Overnight: Cover the cooled cheesecake and refrigerate it overnight.
Remove from the Pan: Carefully release the chilled cheesecake from the springform pan.
Slice the Cheesecake: Cut the cheesecake into slices for serving.
Add the Topping: Spoon the reserved blueberry-and-sauce mixture over the slices and add whipped cream if desired.
