Preheat your oven to 350°F (175°C) and grease a 9-inch springform pan. In a mixing bowl, combine the brownie mix with the eggs and oil or butter following package instructions. Pour the mixture into the prepared pan and bake for 20-25 minutes until a toothpick comes out with slight moist crumbs.

Once the brownie base has cooled, lower the oven temperature to 325°F (160°C). In a large mixing bowl, beat the softened cream cheese until smooth, then gradually mix in granulated sugar. Add eggs one at a time, mixing well after each addition, followed by sour cream and heavy cream until the batter is silky and well-combined.

Carefully drizzle caramel sauce over the top of the cheesecake filling in a zigzag pattern. Using a knife or a skewer, gently swirl the caramel into the cheesecake mixture, creating beautiful marbling.

Pour the cheesecake mixture over the cooled brownie base, smoothing the top with a spatula. Bake for 50-60 minutes, or until the edges appear set and the center slightly jiggles. Turn off the oven but leave the cheesecake inside for an additional hour to cool gradually.

After an hour, remove the cheesecake from the oven and allow it to cool to room temperature. Cover it with plastic wrap and refrigerate for at least 4 hours or overnight for best results. Serve topped with additional caramel sauce, whipped cream, and chocolate shavings.