Step 1: Preheat your oven to 350°F (175°C). Grease a 9-inch springform pan.
Step 2: For the brownie layer: In a large microwave-safe bowl (or a saucepan), melt the butter. Stir in the granulated sugar until well combined.
Step 3: Whisk in the eggs one at a time, ensuring each is fully incorporated. Then, stir in the vanilla extract.
Step 4: In a separate bowl, sift together the flour, cocoa powder, and salt.
Step 5: Gradually add the dry ingredients to the wet ingredients, mixing just until no streaks of flour remain. Do not overmix.
Step 6: Pour the brownie batter into the prepared springform pan. Smooth out the top with a spatula.
Step 7: Bake the brownie layer for 25-30 minutes, until a toothpick inserted comes out with moist crumbs. Remove from oven and let cool completely.
Step 8: While the brownie cools, prepare the cheesecake layer: In a large mixing bowl, beat the softened cream cheese and sugar together until smooth and creamy. Scrape down the sides of the bowl.
Step 9: Add the eggs one at a time, beating just until combined after each addition. Gently stir in the vanilla extract and sour cream. Avoid overmixing.
Step 10: Once the brownie layer is completely cool, pour the cheesecake mixture evenly over it.
Step 11: Bake for another 30-35 minutes, until the edges are set and the center still has a slight jiggle. Carefully remove from oven and let cool on a wire rack to room temperature.
Step 12: For the caramel sauce: In a medium saucepan, melt 1 cup sugar over medium heat, stirring occasionally, until it turns a beautiful golden amber color. Do not let it get too dark.
Step 13: Carefully stir in 6 tablespoons butter. It will bubble vigorously; keep stirring until fully melted and incorporated.
Step 14: Slowly pour in 1/2 cup heavy cream while continuously stirring until the mixture is smooth and any lumps have dissolved.
Step 15: Remove the saucepan from the heat and stir in 1 teaspoon sea salt. Taste and adjust if desired.
Step 16: Once the cheesecake is completely cooled to room temperature, generously drizzle the caramel sauce all over the top.
Step 17: Refrigerate for at least 2 hours (ideally longer) to allow it to fully set. Once chilled, release the springform pan sides, slice, and serve.