Place the leftover marinade in a small saucepan and reduce it in half over medium heat. Skim the fats that rise to the top to ensure a clear, smooth sauce. When reduced, strain the marinade into a clean saucepan, then add the peppercorns, brown sugar, and butter over medium heat. Whisk all ingredients to combine. Season the sauce with more salt to taste and set aside.
Cook the flank steak on a hot grill or a plancha/griddle. Cook for about 4 minutes on one side, then turn it over and cook for an additional 4 minutes for medium-rare( 125°F to 130°F).
Cut the flank steak against the grain in thin slices. Serve on a platter with your choice of sides. Pour half of the sauce on the sliced steak and reserve the rest to serve on the side. If desired, sprinkle additional sea salt on steak.