Preheat your oven to 350°F (175°C) and grease a 9-inch springform pan. Follow the package directions for the brownie mix, combining it with eggs, vegetable oil, and water until smooth. Pour the batter into the pan and bake for 25-30 minutes or until a toothpick inserted comes out with a few moist crumbs. Let cool completely.

In a mixing bowl, beat the softened cream cheese with an electric mixer until creamy. Gradually add the granulated sugar and vanilla, and then add the eggs one at a time, mixing well after each addition to achieve a smooth mixture.

Pour the cheesecake mixture over the cooled brownie base, spreading it evenly. Drizzle caramel sauce over the cheesecake and use a toothpick to swirl it in.

Bake for 50-60 minutes. The edges should be set while the center remains slightly jiggly. Turn off the oven, crack the door, and allow the cheesecake to cool inside for 1 hour.

Cool the cheesecake to room temperature on a wire rack. Transfer to the refrigerator and chill for at least 4 hours or overnight before serving.