Preheat your oven to 325°F (163°C). In a mixing bowl, combine the graham cracker crumbs, ¼ cup of sugar, and melted butter until the mixture resembles wet sand. Firmly press this mixture into the bottom of a greased 9-inch springform pan to form a solid crust. Bake for 8-10 minutes until golden and fragrant, then allow it to cool completely while you prepare the filling.

In a large mixing bowl, use an electric mixer to beat the softened cream cheese and 1 cup of sugar together until smooth and creamy. Blend in the sour cream and vanilla extract until well incorporated. Carefully add the eggs, one at a time, mixing on low speed just until combined to prevent overmixing. The filling should be lush and free of lumps.

In a medium saucepan over medium heat, combine the blueberries, 2 tablespoons of sugar, and lemon juice. Cook while gently stirring until the blueberries soften and release their juices, about 5-7 minutes. Stir in a mixture of cornstarch and water, cooking for another minute until the swirl thickens. Remove from heat and let it cool slightly.

Pour the cheesecake batter over the cooled crust, smoothing it out evenly. Drizzle the prepared blueberry swirl on top of the cheesecake mixture, using a skewer to swirl gently for a marbled effect. Bake in the preheated oven for 50-60 minutes. You'll know it's ready when the edges are set and the center still has a slight wobble.

Once baked, turn off the oven and crack the door to let the cheesecake cool slowly for 1 hour. Afterwards, transfer the cheesecake to the fridge and chill for at least 4 hours, or preferably overnight.