In a mixing bowl, combine the graham cracker crumbs, melted butter, and 2 tablespoons of granulated sugar. Stir until the mixture resembles wet sand. Press this mixture into the bottom of a 9-inch springform pan. Bake for 10 minutes, then cool completely.
In a large mixing bowl, beat the softened cream cheese until smooth and creamy, about 2-3 minutes. Gradually add in 1 cup of granulated sugar while continuing to mix until fully blended.
Add the eggs one at a time, mixing on low speed until incorporated. Then add the vanilla extract, lemon zest, and lemon juice, mixing until combined.
In a small bowl, toss the blackberries with cornstarch until lightly coated. Gently fold the blackberries into the cheesecake filling.
Pour the cheesecake filling over the cooled crust. Bake for 50-60 minutes, until the center is slightly jiggly but set.
Turn off the oven and leave the cheesecake inside with the door cracked open for about 1 hour. Then, cool to room temperature, cover, and refrigerate for at least 4 hours or overnight.
Carefully remove the sides of the springform pan. Dust the top with powdered sugar and decorate with additional blackberries before serving.
Notes
For an elegant touch, serve with extra blackberries and a drizzle of lemon zest syrup.