1. Preheat your oven to 325°F (165°C).

2. In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy.

3. Gradually add the granulated sugar and continue mixing until well incorporated.

4. Add the eggs one at a time, beating well after each addition.

5. Slowly pour in the heavy cream and mix until the batter is smooth and well-combined.

6. Grease a 9-inch springform pan and pour the cheesecake batter into it.

7. Bake for 55-65 minutes, or until the center is almost set. The edges should be slightly puffed and golden.

8. Turn off the oven and leave the cheesecake inside with the door ajar for 1 hour.

9. Remove the cheesecake from the oven and let it cool completely on a wire rack.

10. Once cooled, carefully remove the springform ring.

11. In a small saucepan, gently heat the blackberries until they release their juices and become slightly softened, about 5 minutes.

12. Drizzle the warm blackberry sauce over the top of the chilled cheesecake.

13. Refrigerate the cheesecake for at least 4 hours, or overnight, before serving.