Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan.
In a large bowl, prepare the brownie mix according to the package instructions using the vegetable oil, eggs, and water. Pour the brownie batter into the prepared springform pan and spread evenly.
Bake the brownie layer for 20 minutes. Remove from the oven and let it cool slightly while you prepare the cheesecake layer.
In a mixing bowl, beat the softened cream cheese until smooth. Add the granulated sugar, vanilla extract, and salt, mixing until well combined.
Add the eggs one at a time, mixing well after each addition. Then, stir in the sour cream and 1/2 cup of caramel sauce until smooth. If desired, fold in the chocolate chips.
Pour the cheesecake mixture over the baked brownie layer in the springform pan, spreading it evenly.
Bake for an additional 45-50 minutes, or until the center is set but slightly jiggly. Turn off the oven and crack the door, letting the cheesecake cool in the oven for 1 hour.
Remove from the oven and refrigerate for at least 4 hours or overnight to set completely.
Before serving, drizzle additional caramel sauce over the top and slice into pieces.