1. Preheat the oven to 325°F and line the bottom of a 9-inch springform pan with parchment paper. Lightly grease the sides.

2. Melt the butter and semi-sweet chocolate together in a heatproof bowl until smooth. Let it cool slightly.

3. Whisk 1 1/4 cups granulated sugar into the chocolate mixture.

4. Add 2 eggs and 1 teaspoon vanilla extract, whisking until glossy.

5. Stir in the flour, cocoa powder, and salt just until combined.

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

7. Bake for 18 to 20 minutes, until the top is set but the center is still slightly soft. Let cool for 10 minutes.

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

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

10. Add the remaining 2 eggs one at a time, mixing on low speed.

11. Mix in the remaining 1 teaspoon vanilla extract, sour cream, and heavy cream until smooth.

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

13. Bake for 45 to 50 minutes, until the edges are set and the center still has a slight wobble.

14. Turn off the oven, crack the door slightly, and let the cheesecake sit inside for 20 minutes.

15. Remove from the oven and cool completely at room temperature.

16. Refrigerate for at least 6 hours, preferably overnight, before slicing and serving.