Preheat the oven to 325°F and grease a 9-inch springform pan with nonstick spray. In a large mixing bowl, combine the melted butter, granulated sugar, cocoa powder, and fine salt. Stir the mixture thoroughly until it's well-blended. Once the mixture has cooled slightly, mix in the vanilla extract. Add the eggs one at a time, making sure to stir thoroughly after each addition. When the mixture is smooth, incorporate the flour and stir until combined. Evenly spread the brownie batter in the prepared pan.

Bake the brownie layer for about 15 minutes, or until it's just beginning to set but still slightly underdone. Remove the pan from the oven and let it cool to room temperature. Once cooled, refrigerate the brownie layer while preparing the cheesecake portion. Keep the oven at 325°F if proceeding directly to the cheesecake layer.

Using an electric mixer, beat the cream cheese until smooth, about 1 minute. Gradually add both sugars and the heavy cream, beating until the mixture is well-blended. Scrape down the sides of the bowl to ensure all the cream cheese is fully incorporated. Add the eggs one at a time, mixing gently after each addition just until the batter is smooth. Stir in the vanilla paste or extract.

Pour the cheesecake batter over the chilled brownie layer and gently tap the pan on the counter to eliminate any air bubbles. Place the springform pan on a rimmed baking sheet and bake for 55 minutes to 1 hour. The cheesecake should appear slightly dry on top but can still have a slight wobble in the center. Turn off the oven, crack open the door, and allow the cheesecake to cool inside for 10 minutes. Remove from the oven and transfer to a wire rack to cool completely at room temperature.

Refrigerate the cheesecake for at least 4 hours, or overnight, until fully chilled. Once chilled, release the cheesecake from the springform pan and transfer it to a serving plate or cake stand. Slice and drizzle each portion with salted caramel sauce before serving.