How to Make It
Preheat oven to 350°F with rack in center position. Using baking spray or softened butter, lightly grease an 8-inch square baking pan. Line pan with parchment paper, letting ends extend over rim of pan. (This will enable you to easily lift the brownies from the pan.)
Melt chocolate and butter in top of a double boiler, stirring to combine. Once melted, remove from heat, and set aside to let cool slightly, about 15 minutes.
Whisk sugar and eggs in a large bowl until pale in color, about 1 minute. Add vanilla, kosher salt, and melted chocolate; whisk until combined. Add flour, whisking until just combined and no streaks of flour remain. Pour batter into prepared pan.
Bake in preheated oven until brownies are set and a wooden pick inserted in middle comes out mostly clean (it’s OK if a few crumbs are on the wooden pick), about 35 minutes. Remove from oven, and let cool on a wire rack.
Stir together sugar, 1/2 cup water, and corn syrup in a small saucepan. Cook, without stirring, until mixture boils and turns amber in color, about 10 minutes. Remove caramel from heat, and immediately drizzle in cream, stirring constantly. (It will bubble and sputter, but the cream will halt the cooking process and prevent the caramel from taking on further color and burning.) Stir in butter and kosher salt, and return saucepan to heat over medium. Simmer 1 minute, allowing caramel to thicken slightly. Transfer to a bowl.
Once brownies are completely cool, lift them from pan, and place on a serving plate. Spoon desired amount of salted caramel on top of brownies. Cut into 16 squares. Sprinkle with sea salt, if desired. Brownies can be stored in an airtight container at room temperature up to 3 days.