Season the flank steak with 1 tsp. of the salt and the pepper. Mix 1 Tbs. of the soy sauce, 1 Tbs. of the canola oil, 2 Tbs. of the ginger, and 1 Tbs. of the garlic in a large zip-top plastic bag. Add the steak and turn and massage it in the bag to cover it with the marinade. Refrigerate for at least 4 hours or as long as overnight.
Heat 1-1/2 Tbs. of the canola oil and the remaining 2 Tbs. ginger and 1/2 Tbs. garlic in a small saucepan over medium heat until the ginger and garlic sizzle steadily and just begin to brown around the edges, about 3 min. Add 1/3 cup water, the remaining 1/4 cup soy sauce, and the rice vinegar, sesame oil, and brown sugar. Bring to a boil over medium-high heat. In a small bowl, whisk the cornstarch with 2 tsp. of water and stir it into the soy mixture. Cook until it returns to a boil and thickens slightly, about 1 min. Remove from the heat and set aside.
Heat a gas grill to medium high or prepare a fire on a charcoal grill with a medium-hot and a low zone. Rinse the scallions but do not dry them. Toss the scallions with the remaining 1-1/2 Tbs. canola oil and 1/2 tsp. salt.
Clean and oil the grill grates. Grill the steak (over the hotter zone if using charcoal), covered, until it has good grill marks, 5 to 6 min. Flip and reduce the heat to medium if using a gas grill or transfer the steak to the cooler part of the charcoal fire. Cook, covered, until the steak is done to your liking, 4 to 5 min. for medium rare (cut into the steak to check). Transfer to a large cutting board, brush with about a third of the sesame sauce, and let rest for 5 to 10 min.
While the steak rests, clean and oil the grill grates, set the scallions on the grill (over the cooler zone if using charcoal), and cook until they have good grill marks, 2 to 4 min. Flip and cook until they’re tender, 2 to 4 min. Transfer to a large platter and drizzle with a couple of tablespoons of the sesame sauce.
Slice the steak thinly and serve with the scallions, a drizzle of the remaining sesame sauce, and a sprinkling of sesame seeds.