Make the salted caramel: In a saucepan over medium heat, melt 1 cup sugar without stirring, swirling pan occasionally until amber colored. Remove from heat and carefully whisk in warmed heavy cream (mixture will bubble vigorously). Stir in 4 tablespoons butter and 1 teaspoon sea salt until smooth. Let cool for 15 minutes.

Preheat oven to 350°F. Line a 9x13-inch baking pan with parchment paper, leaving overhang on sides for easy removal.

Melt 1 cup butter and chopped dark chocolate together in microwave or double boiler, stirring until smooth. Let cool slightly. Whisk in 1-1/2 cups sugar until combined. Add eggs one at a time, whisking well after each. Stir in vanilla extract.

Sift together flour, cocoa powder, and 1/2 teaspoon salt. Fold into chocolate mixture just until no flour streaks remain. Don't overmix. Pour batter into prepared pan and smooth top.

Drizzle cooled caramel over brownie batter in lines. Use a knife to swirl caramel through batter, creating marbled effect. Sprinkle with flaky sea salt. Bake for 30-35 minutes until toothpick inserted in center comes out with a few moist crumbs.

Let brownies cool completely in pan on wire rack, at least 1 hour. Use parchment overhang to lift out entire brownie slab. Cut into 16 squares with a sharp knife, wiping knife clean between cuts for neat edges.