Preheat your oven to 350°F (175°C). Grease a 9-inch springform pan and line the bottom with parchment paper.
In a medium saucepan, melt the butter over low heat. Remove from heat and stir in the sugar, eggs, and vanilla until well combined. Sift together the flour, cocoa powder, baking powder, and salt; gradually stir into the butter mixture until just combined. Pour the brownie batter into the prepared springform pan, spreading it evenly.
Bake the brownie layer for 20 minutes, then remove from the oven and allow to cool slightly while you prepare the cheesecake layer.
In a large mixing bowl, beat the softened cream cheese until smooth. Gradually add the sugar, mixing well after each addition. Add the eggs, one at a time, mixing until just combined, then stir in the vanilla and sour cream.
Pour the cheesecake batter over the cooled brownie layer in the springform pan, spreading it evenly on top.
Bake for 45-50 minutes or until the edges are set and the center has a slight jiggle. Turn off the oven and leave the cheesecake inside for an additional hour with the door slightly cracked.
Refrigerate the cheesecake for at least 4 hours or overnight for best results.
In a medium saucepan over medium heat, combine the sugar. Stir constantly until it melts into a golden-brown liquid. Carefully add the butter and stir until melted. Slowly pour in the heavy cream while whisking—it will bubble up! Stir in the salt and let the sauce cool for a few minutes before drizzling over the cheesecake.
Remove the cheesecake from the springform pan. Drizzle with caramel sauce before slicing and serving.