Prep Marinade: In a mixing bowl, combine soy sauce, water, brown sugar, rice vinegar, sesame oil, grated ginger, and minced garlic.
Marinate Salmon: Place the salmon fillets in the marinade and let them sit for at least 30 minutes in the refrigerator.
Preheat Grill: Heat the grill to medium-high heat.
Grill Salmon: Remove salmon from marinade and grill each side for about 6 minutes or until the fish flakes easily with a fork.
Thicken Sauce: While the salmon is grilling, pour the remaining marinade into a small pan, add cornstarch mixture, and bring to a simmer until thickened.
Serve: Place grilled salmon on a plate, drizzle with thickened teriyaki sauce, and garnish with green onions and sesame seeds.