Step 1: Preheat oven to 350°F (175°C). Grease a 9-inch springform pan. Prepare brownie mix according to package directions. Pour batter into the prepared springform pan.
Step 2: Bake brownie for 20-25 minutes, or until a toothpick inserted into the center comes out with moist crumbs. Do not overbake. Let cool completely on a wire rack.
Step 3: Reduce oven temperature to 325°F (160°C). Wrap the bottom and sides of the springform pan with heavy-duty foil to prevent water from seeping in during the water bath.
Step 4: In a large bowl, beat softened cream cheese with granulated sugar until smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl.
Step 5: Beat in eggs one at a time, mixing on low speed just until combined after each addition. Do not overmix.
Step 6: Stir in sour cream, vanilla extract, and salt until just incorporated. Pour the cheesecake batter over the cooled brownie base in the springform pan.
Step 7: Place the foil-wrapped springform pan into a larger roasting pan. Pour hot water into the roasting pan until it reaches halfway up the sides of the springform pan.
Step 8: Carefully transfer the pans to the preheated oven. Bake for 60-75 minutes, or until the edges are set and the center still has a slight wobble.
Step 9: Turn off the oven, crack the door open, and let the cheesecake cool in the oven for 1 hour. Remove from oven, remove foil, and let cool completely on a wire rack.
Step 10: Once cooled, refrigerate the cheesecake for at least 6-8 hours, or preferably overnight, until thoroughly chilled and set.
Step 11: Before serving, warm the caramel sauce slightly if it's too thick. Drizzle generously over the top of the chilled cheesecake and swirl gently with a knife or spoon for a decorative effect. Slice with a hot, clean knife for perfect pieces.