Step 1: To make the brown butter, melt 1 cup (226g) unsalted butter in a light-colored saucepan over medium heat. Stir occasionally as it melts.
Step 2: Continue cooking, stirring frequently, until the butter foams, then subsides, and golden-brown flecks appear at the bottom. It will smell nutty. Immediately remove from heat and pour into a heatproof bowl, scraping all brown bits. Set aside to cool slightly.
Step 3: For the salted caramel, combine 1 cup (200g) granulated sugar and 1/4 cup (60ml) water in a heavy-bottomed saucepan. Cook over medium heat without stirring until sugar dissolves and mixture boils.
Step 4: Continue cooking, swirling the pan occasionally (do not stir with a spoon), until the syrup turns a deep amber color.
Step 5: Carefully and slowly pour 1/2 cup (120ml) heavy cream into the hot caramel while whisking constantly. The mixture will bubble vigorously. Continue to whisk until smooth.
Step 6: Remove from heat and stir in 2 tablespoons (28g) unsalted butter and 1 teaspoon flaky sea salt. Let cool slightly while preparing the brownie batter.
Step 7: Preheat your oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, leaving an overhang on the sides.
Step 8: To the cooled brown butter, add 1 cup (200g) granulated sugar and 1/2 cup (100g) packed light brown sugar. Whisk until well combined and glossy.
Step 9: Whisk in the 3 large eggs, one at a time, ensuring each is fully incorporated before adding the next. Stir in 1 teaspoon vanilla extract.
Step 10: In a separate bowl, whisk together 1 cup (125g) all-purpose flour, 3/4 cup (75g) unsweetened cocoa powder, 1/2 teaspoon baking powder, and 1/2 teaspoon salt.
Step 11: Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix.
Step 12: Fold in the 1 cup (170g) of chopped bittersweet or semi-sweet chocolate.
Step 13: Pour half of the brownie batter into the prepared pan and spread evenly. Drizzle about half of the cooled salted caramel over the batter and gently swirl with a knife or skewer.
Step 14: Pour the remaining brownie batter over the caramel layer and gently spread to cover. Drizzle the remaining caramel on top and swirl again.
Step 15: Bake for 35-40 minutes, or until a toothpick inserted into the center comes out with moist crumbs, but not wet batter. Do not overbake.
Step 16: Let the brownies cool completely in the pan on a wire rack before lifting out using the parchment paper overhang and cutting into squares. This ensures ultimate fudginess.