Preheat your oven to 325°F (163°C).

In a mixing bowl, combine graham cracker crumbs, melted butter, and sugar. Mix until the crumbs are moist.

Press the crumb mixture firmly into the bottom of a 9-inch springform pan to form an even crust. Bake for 10 minutes, then remove from the oven and let it cool.

In a separate mixing bowl, beat the softened cream cheese until smooth using an electric mixer. Gradually add sugar and continue to mix until creamy.

Add the vanilla extract and mix. Then, add the eggs one at a time, mixing just until combined after each addition.

Stir in the sour cream and flour until fully incorporated. Be careful not to overmix.

Pour the cheesecake batter onto the cooled crust and spread it evenly.

Bake in the preheated oven for 50-60 minutes, or until the center is set but slightly jiggly. Turn off the oven and let the cheesecake cool inside with the door slightly ajar for an hour.

While the cheesecake cools, prepare the blackberry sauce. In a saucepan over medium heat, combine blackberries, sugar, and lemon juice. Cook until the blackberries start to break down (about 5-7 minutes).

If a thicker sauce is desired, mix cornstarch with a tablespoon of water and add it to the saucepan, stirring well. Cook for an additional 2-3 minutes until thickened.

Strain the sauce through a fine mesh sieve to remove the seeds, pressing down with a spatula to extract as much liquid as possible. Set the sauce aside to cool.

Once the cheesecake has completely cooled, refrigerate for at least 4 hours or overnight.

Before serving, top the cheesecake with the cooled blackberry sauce and fresh blackberries if desired. Slice and enjoy!