1. In a large bowl, combine ground beef, chopped scallions, 4 tablespoons of sesame teriyaki sauce, 3 tablespoons of sesame seeds, breadcrumbs, egg, and water. Mix well, then cover and chill for 20 minutes.
2. Whisk 1 cup of sesame teriyaki sauce and 2 teaspoons of sesame oil together to make the marinade.
3. Prepare the mushrooms by cleaning and drying them, removing the stems. Place the mushrooms, green pepper pieces, and red onion chunks in a separate bowl. Add half of the marinade to the vegetables and toss to coat, then set aside.
4. Shape the chilled meat mixture into 48 small meatballs. Place them in a baking pan and pour the remaining marinade over them, turning gently to coat. Return the pan to the refrigerator and chill for another 20 minutes until firm enough for skewering.
5. Soak wooden skewers in water for at least 20 minutes to prevent burning.
6. Preheat your grill to medium-high heat and lightly oil the grates.
7. Alternate threading the chilled meatballs and prepared vegetables onto the skewers.
8. Grill the skewers for 10-12 minutes, turning them periodically, until the meatballs are browned and cooked through, and the vegetables are crisp-tender.
9. If baking, preheat your oven to 425 degrees Fahrenheit (220 degrees Celsius) and line a baking sheet with aluminum foil.
10. Thread the chilled meatballs and vegetables onto the soaked skewers and arrange them on the prepared baking sheet. Bake for 18-20 minutes, turning halfway through, until the meatballs are cooked through and the vegetables are lightly caramelized.
11. Finish by drizzling with warm teriyaki sauce and sprinkling with additional sesame seeds.