Prepare the Brownie Base:

1. Preheat oven to 325°F (163°C) and line a 9-inch springform pan with parchment paper.
2. In a mixing bowl, whisk together melted butter, sugar, and vanilla extract until smooth.
3. Add eggs one at a time, mixing well after each addition.
4. Sift in flour, cocoa powder, salt, and baking powder, then gently fold everything together.
5. Pour the batter into the pan and smooth the top.
6. Bake for 15-18 minutes until set but not overbaked. Let it cool.

2. Make the Cheesecake Filling:

1. In a bowl, beat cream cheese and sugar until smooth.
2. Add eggs one at a time, mixing on low speed.
3. Stir in vanilla extract and sour cream until well combined.
4. Pour the cheesecake batter over the cooled brownie layer.

3. Bake the Cheesecake:

1. Wrap the outside of the pan with aluminum foil.
2. Place it in a larger baking dish and add hot water halfway up the sides.
3. Bake at 325°F (163°C) for 45-50 minutes, until the center is slightly jiggly.
4. Turn off the oven and let it cool inside with the door slightly open for 30 minutes.
5. Remove from the water bath and cool at room temperature before refrigerating for 6 hours or overnight.

4. Prepare the Caramel Sauce:

1. In a saucepan, heat the sugar over medium heat, stirring until golden brown.
2. Add the butter, stirring until incorporated.
3. Slowly pour in the heavy cream, stirring continuously.
4. Remove from heat and add salt. Let it cool slightly.

5. Assemble and Serve:

1. Remove the cheesecake from the pan.
2. Pour cooled caramel sauce over the top.
3. Pipe whipped cream on top and sprinkle with chocolate shavings.
4. Slice and serve chilled.