In a small bowl combine 4 teaspoons of the sesame seeds with the salt. Set aside.
In a food processor or blender combine the remaining 4 teaspoons sesame seeds with the marinade ingredients. Blend until almost smooth. Pour half of the marinade into a small saucepan and set aside. Place the steaks in a large resealable plastic bag and pour in the remaining marinade. Press the air out of the bag and seal tightly. Turn the bag to distribute the marinade, place on a rimmed baking dish, and refrigerate for 2 to 4 hours, turning the bag occasionally and massaging the marinade into the steaks. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
Prepare the grill for direct cooking over high heat (450° to 550°F).
Brush the cooking grates clean. Remove the steaks from the bag and discard the marinade in the bag. Grill the steaks over direct high heat, with the lid closed, until cooked to your desired doneness, 6 to 8 minutes for medium rare, turning once or twice. During the last 2 minutes of grilling time, grill the scallions over direct heat, turning once. Remove from the grill and let the steaks rest for 3 to 5 minutes.
While the steaks rest, make the sauce. Place the small saucepan with the marinade over medium-high heat and bring to a boil. Boil until slightly thickened and reduced to about ½ cup, about 5 minutes, stirring frequently.
Cut the steaks into thin slices. Drizzle with the reduced marinade and sprinkle with sesame salt. Serve warm with grilled scallions.