1. Preheat the oven to 350°F and grease a 9-inch springform pan, then line the bottom with parchment paper.

2. In a mixing bowl, whisk together the melted butter and 1 3/4 cups granulated sugar until glossy.

3. Add 3 eggs and 2 teaspoons vanilla extract, then whisk until smooth.

4. Stir in the cocoa powder, flour, and salt just until no dry streaks remain.

5. Spread the brownie batter evenly into the prepared pan.

6. Bake the brownie layer for 18 to 20 minutes, until the top is set but the center is still slightly soft.

7. Let the brownie base cool for 10 minutes while you prepare the cheesecake filling.

8. In a large bowl, beat the softened cream cheese until completely smooth.

9. Add 3/4 cup granulated sugar and mix until combined.

10. Beat in 3 eggs one at a time, then mix in 1 teaspoon vanilla extract and the sour cream until the filling is creamy.

11. Pour the cheesecake filling over the brownie layer and smooth the top.

12. Bake for 40 to 45 minutes, until the edges are set and the center has a slight jiggle.

13. Turn off the oven, crack the oven door, and let the cheesecake rest inside for 15 minutes.

14. Remove the cheesecake and let it cool completely at room temperature.

15. Refrigerate for at least 6 hours or overnight.

16. Heat the heavy cream until steaming but not boiling, then pour it over the chocolate chips.

17. Let it sit for 2 minutes, then stir until smooth and glossy.

18. Spread the ganache over the chilled cheesecake.

19. Dust lightly with powdered sugar if desired.

20. Slice and serve chilled.