In a small bowl, whisk together soy sauce, mirin, brown sugar, rice vinegar, garlic, ginger, and cornstarch until smooth. Cut four 12x18 inch sheets of heavy-duty foil. Slice the flank steak as thin as you can against the grain - this is crucial for tenderness. Prep all vegetables so they're ready to go.

Lay one foil sheet on your counter. Place one-quarter of the broccoli, bell pepper, and carrots in the center. Drizzle with a few drops of oil and a pinch of salt. Top with one-quarter of the beef slices. Spoon 2 tablespoons of teriyaki sauce over the beef. Bring the long sides of the foil together and fold down twice to seal, then fold in the ends to create a tight packet. Repeat with remaining ingredients.

To grill: Place packets directly on grates over medium-high heat, close lid, and cook 12-14 minutes. To bake: Arrange on a rimmed baking sheet and bake at 425°F for 18-20 minutes. The packets should puff up and you should hear active sizzling. Carefully open one packet away from your face - the beef should be cooked through and vegetables tender-crisp.

Transfer contents of each packet to a shallow bowl or plate, pouring any accumulated sauce over the top. Sprinkle with sesame seeds and scallions. Serve immediately with steamed rice if desired.