In a mixing bowl, combine 1 ½ cups of graham cracker or vanilla wafer crumbs with 3 tablespoons of sugar and 4 tablespoons of melted butter. Mix until coated and press into the bottom of a 9-inch springform pan.
In a small saucepan, combine 2 cups of fresh blueberries, ¼ cup of water, and 1 tablespoon of cornstarch. Heat over medium, stirring until blueberries burst and mixture thickens. Let cool slightly.
In a large bowl, beat 16 oz of softened cream cheese with ¾ cup of sugar until smooth. Add 1 teaspoon of vanilla and mix. Add 3 eggs one at a time, mixing on low until just combined.
Pour half the cheesecake filling into the crust. Spoon dollops of blueberry sauce over the filling and pour the remaining cheesecake mixture on top. Swirl with a knife for a marbled effect.
Preheat oven to 325°F (160°C). Bake for 55-60 minutes, until edges are set but center jiggles slightly. Turn off oven and cool in the oven for 1 hour.
Once cooled to room temperature, refrigerate for at least 4 hours or overnight. Remove sides of springform pan, slice, and enjoy!