Step 1: Preheat your oven to 350°F (175°C) and line an 8×8 inch baking pan with parchment paper, leaving an overhang on two sides.
Step 2: For the brownie layer: In a medium mixing bowl, whisk together the melted butter and 1 cup granulated sugar until smooth. Beat in the 2 large eggs and 1 teaspoon vanilla extract until well combined. Sift in the cocoa powder, all-purpose flour, and 1/4 teaspoon salt. Stir gently until just combined. Pour the batter into the prepared pan and spread evenly.
Step 3: For the cheesecake layer: In a separate bowl, beat the softened cream cheese with 1/4 cup granulated sugar until light and fluffy. Mix in the remaining 1 large egg and 1 teaspoon vanilla extract until fully incorporated. Carefully pour the cheesecake mixture over the brownie layer, spreading it gently.
Step 4: Bake in the preheated oven for 30-35 minutes, or until the cheesecake layer is set around the edges but still has a slight jiggle in the center. Allow the bars to cool in the pan for 15-20 minutes, then transfer to a wire rack to cool completely.
Step 5: For the salted caramel: In a medium, heavy-bottomed saucepan, melt 1 cup granulated sugar over medium heat, stirring occasionally, until it turns an amber color. Remove from heat. Carefully stir in the 6 tablespoons of butter until melted. Slowly pour in the 1/2 cup heavy cream, stirring constantly until smooth. Stir in the 1/2 teaspoon sea salt. Allow the caramel to cool slightly but remain pourable.
Step 6: Once the brownie and cheesecake layers are completely cool, pour or drizzle the slightly cooled salted caramel evenly over the top. Sprinkle with extra sea salt if desired. Refrigerate for at least 1 hour, or until the caramel has set.
Step 7: Once thoroughly chilled, lift the bars out of the pan using the parchment paper. Place on a cutting board and use a sharp, warm knife to slice into squares. Serve chilled or at room temperature.