Step 1: Preheat your oven to 350°F (175°C). Line a 9-inch springform pan with parchment paper on the bottom and lightly grease the sides.
Step 2: In a heatproof bowl set over a saucepan of simmering water (or in a microwave-safe bowl), melt 1 cup (2 sticks) unsalted butter with 1 cup unsweetened chocolate. Stir until smooth. Remove from heat and let cool slightly.
Step 3: In a large bowl, whisk together 2 large eggs, 1 1/2 cups granulated sugar, and 1 teaspoon vanilla extract until well combined.
Step 4: Gradually add the cooled chocolate mixture to the egg mixture, mixing until just combined.
Step 5: Sift together 1 cup all-purpose flour, 1/2 cup unsweetened cocoa powder, 1/2 teaspoon baking powder, and 1/4 teaspoon salt. Gradually fold the dry ingredients into the wet ingredients until just combined. Be careful not to overmix.
Step 6: Pour the brownie batter into the prepared springform pan, spreading evenly. Bake for 20-25 minutes, or until the edges are set but the center is still slightly soft. A toothpick inserted into the center should come out with moist crumbs, not wet batter. Let cool completely in the pan on a wire rack. This is crucial for the stability of your Caramel Brownie Cheesecake base.
Step 7: Reduce oven temperature to 325°F (160°C). Prepare a water bath by wrapping the bottom of the springform pan securely with heavy-duty aluminum foil to prevent water from seeping in. Place it in a larger roasting pan.
Step 8: In a large bowl, beat 3 (8-ounce) packages full-fat cream cheese (room temperature) with 1 1/4 cups granulated sugar until smooth and creamy. Scrape down the sides of the bowl as needed.
Step 9: Beat in 4 large eggs, one at a time, mixing well after each addition. Do not overbeat, as this can incorporate too much air, leading to cracks.
Step 10: Stir in 1/2 cup sour cream (room temperature) and 1 teaspoon vanilla extract until just combined.
Step 11: Pour half of the cheesecake batter over the cooled brownie base.
Step 12: Drizzle about 1/2 cup of your homemade (or high-quality store-bought) caramel sauce over the cheesecake layer. Use a butter knife or skewer to gently swirl the caramel into the batter.
Step 13: Pour the remaining cheesecake batter over the caramel layer. Drizzle another 1/4 cup of caramel sauce on top and swirl again.
Step 14: Carefully pour hot water into the roasting pan around the springform pan, reaching about halfway up the sides of the springform.
Step 15: Bake for 60-75 minutes, or until the edges are set but the center still has a slight wobble when gently shaken.
Step 16: Turn off the oven, crack the door open slightly, and leave the cheesecake in the water bath for 1 hour. This slow cooling helps prevent cracks.
Step 17: Carefully remove the cheesecake from the water bath and the roasting pan. Remove the foil. Let it cool completely on a wire rack, then cover loosely and refrigerate for at least 6 hours, or preferably overnight, before serving. Chilling is essential for the structure and flavor of your Caramel Brownie Cheesecake.
Step 18: Before serving, gently run a thin knife around the edge of the springform pan before releasing the sides.
Step 19: Drizzle generously with additional homemade caramel sauce. You can warm the sauce slightly to make it easier to pour.
Step 20: Optionally, sprinkle with a pinch of sea salt for a salted caramel brownie cheesecake effect, or add chocolate shavings. Enjoy your magnificent Caramel Brownie Cheesecake!