Step 1: Preheat the Oven

1. Preheat your oven to 325°F (160°C). Grease a 9-inch springform pan.

Step 2: Prepare the Crust

1. In a medium bowl, combine the graham cracker crumbs, sugar, and melted butter. Mix until well combined.
2. Press the mixture firmly into the bottom of the prepared springform pan. Bake for 10 minutes, then remove and let cool.

Step 3: Prepare the Cheesecake Filling

1. In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy.
2. Gradually add the sugar and vanilla extract, mixing until well combined.
3. Add the eggs one at a time, mixing on low speed after each addition until just combined.
4. Mix in the sour cream and flour until smooth.

Step 4: Assemble and Bake

1. Pour the cheesecake filling over the cooled crust in the springform pan.
2. Bake in the preheated oven for 50–60 minutes, or until the center is set but still slightly jiggly. Turn off the oven and let the cheesecake cool in the oven with the door ajar for about 1 hour.

Step 5: Prepare the Berry Topping

1. In a small saucepan, combine the blackberries, raspberries, sugar, lemon juice, and cornstarch (if using). Cook over medium heat for about 5–7 minutes, until the berries are softened and the mixture is slightly thickened.
2. Remove from heat and let the berry topping cool.

Step 6: Chill and Serve

1. Once the cheesecake has cooled, refrigerate it for at least 4 hours, preferably overnight.
2. Before serving, spread the berry topping over the cheesecake. Carefully remove the sides of the springform pan, slice, and enjoy.