Measure out all the ingredients and place them near the stove. Heat sugar over medium-high heat in a medium sized, heavy bottomed saucepan with high sides. Once sugar begins to melt, gently stir with a heatproof spatula or whisk to help it heat evenly.
When (nearly) all of the sugar has melted and liquid is amber (caramel) colored, add the butter and stir until it has completely melted. CAUTION: hot mixture will bubble up when you add the butter.
Stir in the cream. Again CAUTION, the mixture will foam up considerably and possibly splatter.
Reduce the heat and keep stirring and boiling for 2-3 minutes. To remove any undissolved crystal lumps, pour sauce through a wire sieve into a heatproof bowl. Stir in salt. Caramel sauce will thicken as it cools.
For the brownies:
Melt chocolate and butter in a double boiler over hot, but not boiling, water, stirring often. Alternatively, melt chocolate and butter in a large microwave safe bowl in the microwave at 600 watts for 30 second intervals, stirring in between, until chocolate and butter are smooth. Cool until barely warm. While the chocolate mixture is cooling, preheat oven to 350°F (175°C) and butter a 9x13 inch (23x33 cm) baking pan.
Stir sugar, eggs and vanilla into chocolate mixture. Beat lightly with a rubber spatula until combined. Fold in flour.
Spread brownie batter in prepared pan. Spoon about 10 tablespoons of caramel sauce on top of the brownie batter, and swirl the batters together with a butter knife, going back and forth across the pan. Don’t swirl too much or you’ll lose the marbled effect. Sprinkle flakes of sea salt over the top and then bake brownies for 30 minutes. Remove from the oven and cool in the pan on a wire rack. Serve warm with additional warm caramel sauce and perhaps some vanilla ice cream.