Step 1: Prepare the Crust

1. Preheat the oven to 350°F (175°C).
2. In a medium bowl, mix the graham cracker crumbs, sugar, cinnamon, and melted butter until evenly combined.
3. Press the mixture into the bottom of a 9-inch springform pan. Bake for 10 minutes. Remove from the oven and set aside to cool.

Step 2: Make the Cheesecake Filling

1. In a large bowl, beat the softened cream cheese and sugar until smooth and creamy.
2. Add the vanilla extract and lemon juice. Mix until fully incorporated.
3. Add the eggs one at a time, beating on low speed after each addition.
4. Gently fold in the strained blackberry puree until the filling turns a beautiful purple color.
5. Pour the filling over the prepared crust.

Step 3: Bake the Cheesecake

1. Reduce the oven temperature to 325°F (163°C).
2. Bake the cheesecake for 50-60 minutes or until the edges are set but the center still jiggles slightly.
3. Turn off the oven and leave the cheesecake inside with the door slightly open for an hour to cool gradually.
4. After an hour, remove the cheesecake and let it cool completely at room temperature before refrigerating for at least 4 hours (preferably overnight).

Step 4: Prepare the Blackberry Topping

1. In a small saucepan, combine the blackberries, sugar, and water. Cook over medium heat until the blackberries soften and the mixture starts to bubble.
2. Stir in the cornstarch and cook for 2-3 minutes until thickened.
3. Remove from heat and stir in the lemon juice.
4. Let the topping cool completely before spreading over the chilled cheesecake.

Step 5: Serve

1. Carefully remove the cheesecake from the springform pan.
2. Spread the cooled blackberry topping evenly over the top of the cheesecake.
3. Slice and enjoy!